Quadrilaterals And Proof Worksheet With Answers Page 6

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Answers
1. 44 units
2. 9 units
3. 60º, 120º
4. 4
5.
4 6
6. 2.5
7. 22º, 136º
8. 23.75
9. no
10. no
11. yes
12. 12, 15
13. 60º
14. 18.75
15. 8
16. 3
10 + 4 29
17. 95º
18. 105º
19. 3
20.
21. Yes. QS ≅ SQ (reflexive). This fact, along with the given information means that
ΔPQS ≅ ΔRSQ (SSS ≅). That tells us the corresponding parts are also congruent, so
∠PQS ≅ ∠RSQ and ∠PSQ ≅ ∠RQS. These angles are alternate interior angles, so both
pairs of opposite sides are parallel. Therefore, PQRS is a parallelogram.
22. Yes. Since the figure is as a rhombus, all the sides are congruent. In particular, WZ ≅ WX
and ZY ≅ XY . Also, WY ≅ WY (reflexive), so ΔWZY ≅ ΔWXY (SSS ≅). Congruent
triangles give us congruent parts so ∠ZWY ≅ ∠XWY. Therefore, WY bisects ∠ZWX.
23. Yes. Since the lines are parallel, alternate interior angles are congruent so ∠BDC ≅ ∠ECD.
Also, DC ≅ CD (reflexive) so the triangles are congruent by SAS ≅.
24. Not necessarily, since we have no information about AC .
25. Not necessarily.
26. Yes. Because MIFH is a parallelogram, we know several things. First, ∠TME ≅ ∠SFE
(alternate interior angles) and ME ≅ EF (diagonals of a parallelogram bisect each other).
Also, ∠TEM ≅ ∠SEF because vertical angles are congruent. This gives us ΔMTE ≅ ΔFSE
by ASA ≅. Therefore, the corresponding parts of the triangle are congruent, so ES ≅ ET .
27. Since DSIA is a parallelogram, DS AI which gives us ∠D ≅ ∠IAV corresponding angles).
Also, since IA ≅ IV , ΔAIV is isosceles, so ∠IAV ≅ ∠V. The two angle congruence
statements allow us to conclude that ∠D ≅ ∠V.
28. Yes. By the Triangle Midsegment Theorem (see the Math Notes box in Lesson 7.2.6),
since A, W, and K are midpoints of TS , SE , and ET respectively, AW TE and KW TS .
Therefore TAWK is a parallelogram.
102
Core Connections Geometry

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