Mrs. Rivas
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H om ew ork Mrs. Rivas . Complete each congruence statement 1. 3. 5. 7. 2. 4. 6. 8. Lesson 4-1 ∠ ∠ ∆ ∆ ∠
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Mrs. Rivas. Lesson 4-1. . Complete each congruence statement. 1. 2. 3. 4. 5. 6. 7. 8. Mrs. Rivas. Lesson 4-1. State whether the figures are congruent. Justify your answers. 9. Yes ; corresponding sides and corresponding angles are ≅. Mrs. Rivas. Lesson 4-1. - PowerPoint PPT Presentation
Transcript of Mrs. Rivas
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.
