Chapter 4 Review

Report
Homework
Lesson 4-1
∆ ≅ ∆. Complete each congruence statement
1.  ≅ ∠
2.  ≅ 
3.  ≅ ∠
4.  ≅ 
5. ∆ ≅ ∆
6.  ≅ 
7. ∆ ≅ ∆
8. ∠ ≅ ∠
Mrs. Rivas
Homework
Mrs. Rivas
Lesson 4-1
State whether the figures are congruent. Justify your answers.
9. ∆; ∆
Yes; corresponding sides and corresponding angles are ≅.
Homework
Mrs. Rivas
Lesson 4-1
State whether the figures are congruent. Justify your answers.
10. ∆; ∆
No; the only corresponding part that is ≅ is .
Homework
Mrs. Rivas
Lesson 4-1
State whether the figures are congruent. Justify your answers.
11. ⧠; ⧠ 
Yes; corresponding sides and corresponding angles are ≅.
Homework
Mrs. Rivas
Lesson 4-1
State whether the figures are congruent. Justify your answers.
12.∆; ∆
Yes; corresponding sides and corresponding angles are ≅.
Homework
Mrs. Rivas
Lessons 4-2 and 4-3
Can you prove the two triangles congruent? If so, write the congruence
statement and name the postulate you would use. If not, write not possible
and tell what other information you would need.
13.
∠ ≅ ∠
 ≅ 
∠ ≅ ∠

Homework
Mrs. Rivas
Lessons 4-2 and 4-3
Can you prove the two triangles congruent? If so, write the congruence
statement and name the postulate you would use. If not, write not possible
and tell what other information you would need.
14..
 ≅ 
 ≅ 
∠ ≅ ∠

Homework
Mrs. Rivas
Lessons 4-2 and 4-3
Can you prove the two triangles congruent? If so, write the congruence
statement and name the postulate you would use. If not, write not possible
and tell what other information you would need.
15.
 
Homework
Mrs. Rivas
Lessons 4-2 and 4-3
Can you prove the two triangles congruent? If so, write the congruence
statement and name the postulate you would use. If not, write not possible
and tell what other information you would need.
16.
 ≅ 
 ≅ 
 ≅ 

Homework
Lessons 4-2 and 4-3
17. Given:  ≅ ,  bisects  .
Prove: ∆  ∆
 bisects  means that  ≅ .
 ≅  Given
 ≅  Reflective property of ≅
∆ ≅ ∆ SSS
∠ ≅ ∠ Def. of ≅.
 ≅  Reflective property of ≅
∆ ≅ ∆ by SAS.
Mrs. Rivas
Homework
Mrs. Rivas
Lessons 4-2 and 4-3
18. Given: ∠1 ≅ ∠2, ∠3 ≅ ∠4,  ≅ ,
P is the midpoint of .
Prove: ∆ ≅ ∆
It is given that ∠ ≅ ∠ and ∠ ≅ ∠.
By the ⦨ Addition. Post., ∠ ≅ ∠.
Since  is the midpoint of ,  ≅ .
It is given that  ≅ , so ∆ ≅ ∆ by SAS.
Homework
Lesson 4-4
21. Given:  ≅ ,  ∥ 
Prove: ∠ ≅ ∠
 ∥ , so ∠ ≅ ∠.
 ≅  by the Reflexive Prop. of ≅.
Since  ≅ , ∆ ≅ ∆ by SAS,
Then ∠ ≅ ∠ by CPCTC.
Mrs. Rivas
Homework
Lesson 4-4
22. Given: ∠ ≅ ∠, ∠ ≅ ∠
Prove:  ≅ 
 ≅  Reflexive Prop. of ≅.
Since ∠ ≅ ∠ and ∠ ≅ ∠
∆ ≅ ∆ by AAS
 ≅  by CPCTC
Mrs. Rivas
Homework
Mrs. Rivas
Lesson 4-4
23. Given: ∠1 ≅ ∠2, ∠3 ≅ ∠4,
 is the midpoint of 
Prove: ∆ ≅ ∆
∠ ≅ ∠,∠ ≅ ∠ Given
 ≅  Reflexive Property
 is the midpoint of ,   ≅ .
 ≅ 
Reflexive Property
SSS
∆ ≅ ∆
AAS
∆ ≅ ∆
 ≅ 
CPCTC
∠ ≅ ∠ CPCTC
Homework
Mrs. Rivas
Lesson 4-4
24. Given:  = , ∠1 ≅ ∠2,
Prove: ∠ ≅ ∠
∠ ≅ ∠,∠ ≅ ∠ Supplement of ≅ angles are ≅.
 ≅ 
Given
∠ ≅ ∠
Vertical ⦞ are ≅.
∆ ≅ ∆
ASA
∠ ≅ ∠
CPCTC
Homework
Mrs. Rivas
Lesson 4-5
Find the value of each variable
25.



 +  = 
 = 
 = 
Homework
Mrs. Rivas
Lesson 4-5
Find the value of each variable
26.

 +  +  = 
 +  = 
 = 
Homework
Mrs. Rivas
Lesson 4-5
Find the value of each variable
27.
 +  = 
 = 
  base angles
are congruent
 = 
 
 +  = 
 +  = 
 = 
Homework
Mrs. Rivas
Lesson 4-5
28. Given: ∠5 ≅ ∠6,  ≅ 
Prove: ∆ is isosceles.
 ≅ 
Given
∠ ≅ ∠
Isosceles ∆ Theorem
∠ ≅ ∠
≅ Supplement Theorem
∠ ≅ ∠
Given
∆ ≅ ∆
 ≅ 
ASA
CPCTC
and ∆ is isosceles by Isosceles ∆ Theorem
Homework
Mrs. Rivas
Lesson 4-5
29. Given:  ≅ ,  ≅ 
Prove: ∆ is isosceles
 ≅  and  ≅ 
Given
∠ ≅ ∠
Vertical ⦞ are ≅.
∆ ≅ ∆
SAS
∠ ≅ ∠
CPCTC
∠ ≅ ∠ Isosceles ∆ Theorem
∠ + ∠ = ∠ + ∠ Add. Prop. of ≅
so ∠ = ∠ by the ∠ Add. Post. and substitution.
 =  by the Conv. of the Isosceles ∆ Theorem.
∆ is isosceles by Definition of Isosceles ∆.
Homework
Mrs. Rivas
Lessons 4-6 and 4-7
Name a pair of overlapping congruent triangles in each diagram. State
whether the triangles are congruent by SSS, SAS, ASA, AAS, or HL.
30.
∆ ≅ ∆; 
Homework
Mrs. Rivas
Lessons 4-6 and 4-7
Name a pair of overlapping congruent triangles in each diagram. State
whether the triangles are congruent by SSS, SAS, ASA, AAS, or HL.
31.
∆ ≅ ∆; 
Homework
Mrs. Rivas
Lessons 4-6 and 4-7
Name a pair of overlapping congruent triangles in each diagram. State
whether the triangles are congruent by SSS, SAS, ASA, AAS, or HL.
32.
∆ ≅ ∆; 
Homework
Mrs. Rivas
Lessons 4-6 and 4-7
Name a pair of overlapping congruent triangles in each diagram. State
whether the triangles are congruent by SSS, SAS, ASA, AAS, or HL.
33.
∆ ≅ ∆; 
Homework
Mrs. Rivas
Lessons 4-6 and 4-7
34. Given: M is the midpoint of ,
 ⊥ ,  ⊥ , ∠1 ≅ ∠2
Prove: ∆ ≅ ∆
∠ ≅ ∠ Given
 ≅  by the Conv. of the Isosceles ∆ Theorem.
 ≅  by the Def. of Midpoint
 ≅  means that ∠ is a right angle and ∆ is a right ∆.
 ⊥  means that ∠ is a right ⦨ and ∆ is a right ∆ .
∆ ≅ ∆ by HL.
Homework
Mrs. Rivas
35. The longest leg of ∆, , measures 10 centimeters. 
measures 8 centimeters. You measure two of the legs of ∆ and find
that  ≅  and  ≅ . Can you conclude that two triangles to be
congruent by the HL Theorem? Explain why or why not.
No; you only know that two sides (SS) are congruent, and
you don’t know that there are right angles.

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