A Problem Solving Approach to Mathematics for Elementary School Teachers (13th Edition)

Chapter 12

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; From the given diagram, it can be observed that... more

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; Draw a line . ; Mark a line segment of length... more

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; Draw an obtuse angled triangle in which one ... more

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; Since all the sides of the triangle are ... more

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The given triangles are congruent because of the ... more

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No, the triangles may not be congruent as ... more

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Entire Proof Answer: It can be observed that the ... more

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Entire Proof Answer: The sides   and   are equal ... more

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Three or more points are said to be collinear if ... more

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Obtuse triangle ; An obtuse triangle is a triangle... more

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Entire Proof Answer: In   and , the sides   and   ... more

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; Construct a right isosceles triangle. ; Let the... more

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No, it is impossible to make a right triangle with... more

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The point   can be obtained by constructing a ... more

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; Draw a line segment of any length . ; Make an ... more

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; In triangles   and , the sides   and   are ... more

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, , ; In   and , it is given that the sides   and... more

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Theses triangles are congruent because of SSS ... more

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Entire Proof Answer: If diagonal is drawn then ... more

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; In , the sides   and   are equal. So, the ... more

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; In all the sides are congruent, so all angles ... more

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No. If the four points lie on the circle, then ... more

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If four points ,  ,  , and   existed on the same ... more

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; Draw a line segment of any length and label it ... more

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The center of a circle can be constructed by ... more

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No, the triangle cannot be formed using the given ... more

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The remaining side must be less than   and greater... more

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No, the point   does not lie on the circle because... more

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Consider the following concave kite:For part (a):... more

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The given quadrilateral is a kite because one ... more

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YesTaking point away from line and moving ... more

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Entire Proof Answer: In the given figure (b), is ... more

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The rep-tiles contain parallelograms and triangles... more

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Entire Proof Answer: In   and ,   and   are ... more

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It can be completed by first showing that   and   ... more

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If the two figures are congruent, then they must ... more

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For the SAS congruence rule, an angle must be ... more

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No,   and   represents length of the segments. ... more

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Person Z is correct because if   is isosceles, ... more

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No, a quadrilateral cannot be drawn by using the ... more

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Seven non-congruent right triangles ; The non-... more

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If two polygons are identical, then the ... more

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Use the side-side-side (SSS) congruence rule to ... more

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Pair 1: (a) and (h)Pair 2: (b) and (i)Pair 3: (d) ... more

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Entire Proof Answer: Take a quadrilateral .In and... more

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If two angles and an included side of   are given... more

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Join the points and with a line to construct ... more

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The angle required to make the given triangles ... more

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Entire Proof Answer: The sides in the given ... more

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Entire Proof Answer: It is given that   and   is ... more

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Let one of the kites be rhombus and the other be ... more

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When the diagonals of the quadrilateral bisect ... more

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Trapezoids with congruent non-parallel sides are ... more

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Entire Proof Answer: Join the points   and   to ... more

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The resulting figure is a rhombus because all the ... more

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The condition for the sectors of a circle is ... more

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; Draw the first kite by drawing a vertical line ... more

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Rhombus; since all the triangles in the figure are... more

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Any two polygons are said to be congruent if they ... more

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If two angles and an included side of   are given... more

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If all the angles of a quadrilateral   and its ... more

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One included side is required to make the given ... more

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; Use the fact that all the radiuses of a circle ... more

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Entire Proof Answer: Draw a line   such that   and... more

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Entire Proof Answer: In , the angles opposite to ... more

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YesThe construction of two squares with one ... more

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When the diagonals of the quadrilateral are ... more

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Entire Proof Answer: Draw a line   in the given ... more

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YesIf a line segment   is constructed, then two ... more

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; Trapezoids are quadrilaterals, so construct an ... more

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The condition for two rhombi to be congruent is ... more

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No, since no information is given about the sides ... more

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From the given figure, it can be noted that in   ... more

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YesAs the triangle formed by joining the vertices ... more

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The legs of Object B are always selected in which ... more

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Consider an isosceles triangle with base and two... more

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No; as none of the two properties ASA or AAS can ... more

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Entire Proof Answer: Construct an isosceles ... more

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No, because in a parallelogram, each pair of ... more

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Triangles are said to be congruent and not equal ... more

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Due to their rigid shape and strength to support ... more

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The person can extend the shorter sides in one ... more

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The given statement is true as the height of both ... more

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The figure is said incorrect by the teacher due to... more

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Entire Proof Answer: Consider two triangles  and... more

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; Use a ruler to measure the lengths of the given... more

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; Open the compass in such a way that both the ... more

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Draw a line segment of any length using the ... more

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No, it is not because the given figure has 12 ... more

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Entire proof answer: Draw an angle and assume any... more

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; Let there be any two points and on the given ... more

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; To make a copy of the angle , draw a ray . ; ... more

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Extend   line to the left side of point .Place the... more

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; Take the length of on a compass, fix it at , ... more

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Rhombus.In quadrilateral ,   and   are diagonals... more

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Set the compass at point and mark the arc above ... more

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; It is given that and as . is the bisector, so... more

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; and are the points on , which divide into ... more

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About ; Object S acts as the diagonal of a rhombus... more

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Draw a line segment . Take any radius on a compass... more

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Draw a circle by using a compass. Construct the ... more

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; Let there are any two points and on the given... more

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Make two arcs of equal radius from endpoints of ... more

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; Draw a line segment of , and assume that the ... more

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; Draw a line segment   of .Use a protector to ... more

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Use the theorem, which states that the distance of... more

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Draw a perpendicular bisector on line  . Set the ... more

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Use a ruler to draw a side . It will cost .Set the... more

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; Draw a line segment   that is equal to  .Draw a... more

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Draw a line passing through points   and  . Take... more

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; From the given figure,  and   is a transversal... more

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; In a parallelogram opposite sides are equal, so... more

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A trapezoid is a quadrilateral in which one pair ... more

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Yes; When the corresponding angles are equal, the ... more

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Construct a perpendicular to   at point  . Obtain ... more

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Entire Proof Answer: If the diagonals of a ... more

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Join the given points and make a triangle. ... more

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As the measure of angle formed by the lines   and... more

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Place two pieces of the tape along the sides of ... more

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Rhombus; as the angle formed at intersection point... more

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Hello Mr. X,As a syllabus assembler from Saint ... more

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There are various possible constructions that can ... more

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A line cannot be bisected. ; A bisector is a line ... more

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The person is wrong, since the line segments, ... more

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Any one cannot bisect an angle with the only use ... more

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From the given figure,  implies , as alternate ... more

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and are congruent by the AAS congruence property... more

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; The given triangle is an isosceles triangle as ... more

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Yes, the quadrilaterals are congruent using the ... more

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Since   and   are congruent, the pair of the ... more

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Yes, all right triangles with the given conditions... more

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; Let the length of river L be .Since   on the ... more

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; Let the length of the structure be .Since 1 ... more

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Yes, since all the sides of the given rectangles ... more

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Yes, since the corresponding angles of the given ... more

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Each angle in the equilateral triangle measures... more

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    ; Increase the length of each side of the ... more

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; Label the given figure. ; and are given to be... more

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; Follow the below steps to get the required ... more

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; Cross-multiply the given proportion to obtain ... more

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; Draw two hexagons with their sides in ... more

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The machine should be set at approximately . ; The... more

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; Label the given diagram. ; Covert feet into ... more

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; Since , the corresponding sides will be in ... more

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Entire Answer proof: Since   is parallel to and... more

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Yes; The cross sections parallel to the circular ... more

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; Since   corresponds to , create a proportion to... more

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No, it is because the corresponding sides are not ... more

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scale ; 16 feet for the model corresponds to 563 ... more

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No, it is because the sides of the quadrilaterals ... more

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Not necessarily similar as the sides of a square ... more

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Assume a rectangle with sides of 2 and 3 units and... more

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; Assume two right angled isosceles triangles,  ... more

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(a)  is similar to   by SSS similarity; scale ... more

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; is common in all the three triangles, so they ... more

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; Follow the following steps to get the required ... more

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; Let   and   lie end to end on an arbitrary ... more

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; Draw two pentagons with sides in proportion. ; ... more

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; Let   be the length of the original document.It... more

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; Label the given figure. ; Assume   and .and are... more

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; Draw a figure by using the given conditions. ; ... more

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; Observe and . is common in both the triangles... more

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All the semicircles have same shapes, only their ... more

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; Assume that the required distance is .Set up a ... more

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Yes; Any two cubes are always similar as the ratio... more

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Two prisms are similar if their corresponding ... more

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Yes, both the triangles have the same base angles... more

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Let there be two right triangles having hypotenuse... more

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is an equilateral triangle as all the three ... more

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Draw a vertical line on the ruled paper and place... more

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Entire Proof Answer: Use the property of isosceles... more

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The SSS theorem of similarity and that of ... more

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Entire Proof Answer: Since   and   are similar, ... more

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The given proportionality is possible by using the... more

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; Let   be the height of the post,   be the ... more

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Entire Proof Answer: Let there be two similar ... more

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The two triangles  and  are similar. So, the sides... more

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Entire Proof Answer:  bisects into two halves.... more

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Person A is correct and Person B is wrong. Person ... more

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Person M is right. Two right triangles having ... more

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It is not necessary that if one set of the angles ... more

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The student is correct that all  -gons with ... more

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The corresponding sides of the two given triangles... more

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ASA similarity condition is similar to AA ... more

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; Observe the base of the isosceles triangle  be... more

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is the required altitude having the length as... more

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An isosceles triangle with the given measures can ... more

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and are a pair of obtuse vertical angles.The ... more

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Consider the following data:  The graph of the ... more

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The method chosen is indirect measurement method ... more

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Two similar triangles will always have all the ... more

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Parallelogram; This is because it has two pairs of... more

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; Draw a line segment . ; Construct the ... more

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; Assume the point of intersection of   and   to ... more

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; Join the points   and   to form the line ... more

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; The line segments   and ,  and   and   will be ... more

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; Assume two points and on the line .Draw the ... more

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and are not congruent. Both triangles are of ... more

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Entire Proof: Consider and .  and are equal ... more

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; Take two triangles, and .The length of the ... more

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; Mark the points , , , , and in the given ... more

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; Both the triangles have a right angle, that is... more

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No, a quadrilateral will be a square if the ... more

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By the AA similarity ; It is given that .If two ... more

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; If two angles of a triangle are equal, then it ... more

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Entire Proof Answer: The side   is common to both... more

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Draw a scalene triangle .Bisect   by making an arc... more

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: : : Lot ; Find the distance along the ocean ... more

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