1) Select all quadrilaterals for which a diagonal is also a line of symmetry. Write each corresponding letter in the answer box and separate letters with commas.
a) trapezoid b) isosceles trapezoid c) parallelogram d) rhombus e) rectangle f) square
2) Show that diagonal is a line of symmetry for rhombus .
3) is an isosceles trapezoid. Priya makes a claim that triangle is congruent to triangle . Convince Priya this is not true.
4) In quadrilateral , triangle is congruent to . Show that is a parallelogram.
Priya is convinced the diagonals of the isosceles trapezoid are congruent. She knows that if she can prove triangles congruent that include the diagonals, then she will show that diagonals are also congruent. Help her complete the proof.
Given: is an isosceles trapezoid.
Draw auxiliary lines that are diagonals 1 and 2 . is congruent to 3 because they are the same segment. We know angle and 4 are congruent. We know is congruent to 5 . Therefore, triangle and 6 are congruent because of 7 . Finally, diagonal is congruent to 8 because 9 .
Fill in the blanks using items from the Bank of Terms below. Some items might be used more than once.
Bank of Terms: Side-Angle-Side Triangle Congruence Theorem, Corresponding parts of congruent figures are congruent, Triangle , Angle , , , , .
5) Blanks 1 and 2, answers separated by a comma.
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13) Is there enough information in the diagram to prove that triangle is congruent to triangle ?
14) Explain your reasoning.
15) Triangle is isosceles with congruent sides and . Which additional given information is sufficient for showing that triangle is isosceles? Select all that apply. Write each corresponding letter in the answer box and separate letters with commas.
a) Segment is congruent to segment . b) Segment is congruent to segment .
c) Angle is congruent to angle . d) Angle is congruent to angle .
e) is an angle bisector of . f) Triangle is congruent to triangle .