In the figure for Exercise 2, write a statement that the

In Exercises 21 to 24, the triangles named can be proven congruent. Considering the congruent pairs marked, name the additional pair of parts that must be congruent for us to use the method named.

21. SAS

PROOF Statements Reasons 1. and 1. ? 2. ? 2. Identity 3. 3. ? 䉭ABC ⬵ 䉭CDA AD ⬵ CB AB ⬵ CD In Exercises 25 and 26, complete each proof. Use the figure at the top of the second column.

25. Given: and

Prove: 䉭ABC ⬵ 䉭CDA AD ⬵ CB AB ⬵ CD 22. ASA

23. SSS

24. AAS

A D E C B ⌬ABD ⬵ ⌬CBE ⌬WVY ⬵ ⌬ ZVX W X Y Z V ⌬MNO ⬵ ⌬OPM M P N O ⌬ EFG ⬵ ⌬ JHG E F G J H A B D C Exercises 25, 26

26. Given: and

Prove: PROOF Statements Reasons 1. 1. ? 2. 2. ? 3. ? 3. Given 4. ? 4. If two lines are cut by a transversal, alt. int. are 5. 5. ? 6. ? 6. ASA AC ⬵ AC ⬵ ∠s 7 ∠DCA ⬵ ∠BAC DC 7 AB 䉭ABC ⬵ 䉭CDA AD 7 BC DC 7 AB

27. Given: bisects

Prove:

28. Given: and

Prove:

29. Given: and

Prove: 䉭ABC ⬵ 䉭ABD BC ⬵ BD AB ⬜ BD AB ⬜ BC 䉭MQP ⬵ 䉭NQP ∠1 ⬵ ∠2 PQ ⬜ MN 䉭MQP ⬵ 䉭NQP MP ⬵ NP ∠MPN PQ In Exercises 27 to 32, use SSS, SAS, ASA, or AAS to prove that the triangles are congruent. M N P Q 1 2 Exercises 27, 28 C B D A

30. Given: bisects

and are right angles Prove: 䉭PQR ⬵ 䉭NMR ∠Q ∠M MQ PN P Q M N R R S T V Exercises 31, 32

31. Given: and

Prove: 䉭RST ⬵ 䉭SRV RV ⬵ TS ∠VRS ⬵ ∠TSR

37. In quadrilateral ABCD, and are perpendicular

bisectors of each other. Name all triangles that are congruent to: a b c 䉭ABD 䉭ABC 䉭ABE BD AC

41. Given: ;

is the perpendicular bisector of ; is the perpendicular bisector of . Prove: AR ⬵ RC BC RT AB RS ∠ABC

40. Given: and

Prove: and 䉭TPQ ⬵ 䉭VQP 䉭SPV ⬵ 䉭SQT ST ⬵ SV SP ⬵ SQ In Exercises 39 and 40, complete each proof.

39. Given: Plane M

C is the midpoint of and Prove: 䉭ABC ⬵ 䉭DEC AB 7 ED AD ⬜ BE EB

38. In and

, you know that , , and . Before concluding that the triangles are congruent by ASA, you need to show that . State the postulate or theorem that allows you to confirm this statement . ∠B ⬵ ∠E ∠B ⬵ ∠E AB ⬵ DE ∠C ⬵ ∠F ∠A ⬵ ∠D 䉭DEF 䉭ABC

36. Given that and

, does it follow that ? Cite the method, if any, used in reaching this conclusion. 䉭ABC ⬵ 䉭EDC BC ⬵ DC ∠A ⬵ ∠E

34. Given that and

, does it follow that ? Which method, if any, did you use?

35. Given that and

, does it follow that ? If so, cite the method used in arriving at this conclusion. 䉭ABC ⬵ 䉭EDC ∠B ⬵ ∠D ∠A ⬵ ∠E 䉭RST ⬵ 䉭RVU ST ⬵ UV ∠S ⬵ ∠V

32. Given: and

Prove: In Exercises 33 to 36, the methods to be used are SSS, SAS, ASA, and AAS.

33. Given that , does it follow that

is also congruent to ? Name the method, if any, used in arriving at this conclusion. 䉭RVT 䉭RSU 䉭RST ⬵ 䉭RVU 䉭RST ⬵ 䉭SRV ∠TRS ⬵ ∠VSR VS ⬵ TR S V U T R Exercises 33, 34 A B C D E Exercises 35, 36 A B D C E A B C D E F E M B D A C P S Q T V B T C S A R