HomeworkMrs. Rivas

. Complete each congruence statement

1.

3.

5.

7.

2.

4.

6.

8.

Lesson 4-1

∠𝑮 𝑺𝑨

∠𝑻 𝑹𝑬

∆𝑻𝑨𝑺 𝑻𝑺

∆ 𝑨𝑻𝑺 ∠𝑨

HomeworkMrs. Rivas

Lesson 4-1

State whether the figures are congruent. Justify your answers.

9.

Yes; corresponding sides and corresponding angles are ≅.

HomeworkMrs. Rivas

Lesson 4-1

State whether the figures are congruent. Justify your answers.

10.

No; the only corresponding part that is ≅ is

HomeworkMrs. Rivas

Lesson 4-1

State whether the figures are congruent. Justify your answers.

11.

Yes; corresponding sides and corresponding angles are ≅.

HomeworkMrs. Rivas

Lesson 4-1

State whether the figures are congruent. Justify your answers.

12.

Yes; corresponding sides and corresponding angles are ≅.

HomeworkMrs. 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.

∠𝑻 ≅∠𝑺𝑻𝒀 ≅ 𝑺𝑾∠𝒀 ≅∠𝑾

𝑨𝑺𝑨

HomeworkMrs. 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..

𝑬𝑨≅𝑷𝑳𝑨𝑳≅ 𝑳𝑨

∠𝑬𝑨𝑳≅∠𝑷𝑳𝑨

𝑺𝑨𝑺

HomeworkMrs. 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.

𝑵𝒐𝒑𝒐𝒔𝒔𝒊𝒃𝒍𝒆

HomeworkMrs. 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.

𝑪𝑵 ≅ 𝑨𝑶𝑵𝑨≅𝑶𝑪𝑨𝑪 ≅𝑪𝑨

𝑺𝑺𝑺

HomeworkMrs. Rivas

17. Given:, bisects .

Prove:

Lessons 4-2 and 4-3

bisects means that

Given

SSS

Reflective property of ≅

Reflective property of ≅

Def. of .≅

by SAS.

HomeworkMrs. Rivas

18. Given: , , ,

Prove:

P is the midpoint of .

Lessons 4-2 and 4-3

It is given that and .

By the Addition. Post., .

Since is the midpoint of , .

It is given that , so by SAS.

HomeworkMrs. Rivas

Lesson 4-4

21. Given:

Prove:

, so .

by the Reflexive Prop. of .

Since , by SAS,

Then by CPCTC.

HomeworkMrs. Rivas

Lesson 4-4

22. Given: Prove:

Reflexive Prop. of .

by CPCTC

Sinceand

by AAS

HomeworkMrs. Rivas

Lesson 4-4

23. Given: ,

is the midpoint of

Prove:

,Given

Reflexive Property

AAS

CPCTC

is the midpoint

Reflexive Property

SSS

CPCTC

HomeworkMrs. Rivas

Lesson 4-4

24. Given: ,

Prove:

, Supplement of angles are .

Vertical ⦞ are .

Given

ASA

CPCTC

HomeworkMrs. Rivas

Lesson 4-5

Find the value of each variable25.

𝟔𝟎 𝟔𝟎

𝟔𝟎𝟐 𝒙+𝟏𝟎=𝟔𝟎

𝟐 𝒙=𝟓𝟎𝒙=𝟐𝟓

HomeworkMrs. Rivas

Lesson 4-5

Find the value of each variable26.

𝟐𝟓𝟐𝟓+𝟗𝟎+𝒙=𝟏𝟖𝟎𝟏𝟏𝟓+𝒙=𝟏𝟖𝟎

𝒙=𝟔𝟓

HomeworkMrs. Rivas

Lesson 4-5

Find the value of each variable27.

𝒁+𝟏𝟑𝟓=𝟏𝟖𝟎𝒛=𝟒𝟓

𝒙=𝟒𝟓

base angles are congruent 𝑹𝒆𝒎𝒐𝒕𝒆𝒂𝒏𝒈𝒍𝒆𝒔𝒙+𝒚=𝟏𝟑𝟓𝟒𝟓+𝒚=𝟏𝟑𝟓𝒚=𝟗𝟎

HomeworkMrs. Rivas

Lesson 4-5

28. Given:

Prove: is isosceles.

Given

Isosceles ∆ Theorem

≅ Supplement Theorem

Given

ASA

CPCTC

and is isosceles by Isosceles ∆ Theorem

HomeworkMrs. 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 ∆.

HomeworkMrs. 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.

∆ 𝑨𝑹𝑶 ≅∆ 𝑹𝑨𝑭 ;𝑯𝑳

HomeworkMrs. 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.

∆ 𝑹𝑸𝑴≅ ∆𝑸𝑹𝑺 ;𝑺𝑺𝑺

HomeworkMrs. 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.

∆ 𝑨𝑶𝑵 ≅ ∆𝑴𝑶𝑷 ;𝑨𝑨𝑺

HomeworkMrs. 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.

∆𝑮𝑹𝑻 ≅ ∆𝑮𝑺𝑶 ;𝑨𝑺𝑨

HomeworkMrs. Rivas

Lessons 4-6 and 4-7

34. Given: M is the midpoint of ,

Prove:

Given

by the Conv. of the Isosceles ∆ Theorem.

by the Def. of Midpoint

means thatis a right angle and is a right ∆.

means thatis a right and ⦨ is a right ∆ .

by HL.

HomeworkMrs. Rivas

35. The longest leg of ,, measures centimeters. measures 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.