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Homework
4-1 𝑪𝑨𝑻  𝑱𝑺𝑫. List each of the following.
1. three pairs of congruent sides
𝑪𝑨 ≅ 𝑱𝑺
𝑨𝑻 ≅ 𝑺𝑫
𝑪𝑻 ≅ 𝑱𝑫
2. three pairs of congruent angles
∠𝑪 ≅ ∠𝑱
∠𝑨 ≅ ∠𝑺
∠𝑻 ≅ ∠𝑫
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Homework
Mrs. Rivas
Algebra Find the values of the variables.
3.
𝟓𝒙
𝟕𝟒
𝟓𝒙 + 𝟕𝟒 + 𝟑𝒙 + 𝟐 = 𝟏𝟖𝟎
𝟖𝒙 + 𝟕𝟔 = 𝟏𝟖𝟎
𝟖𝒙 = 𝟏𝟎𝟒
𝒙 = 𝟏𝟑
Homework
Algebra Find the values of the variables.
4.
𝟐𝒙 = 𝟏𝟎
𝒙=𝟓
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Homework
Mrs. Rivas
Algebra ABCD  FGHJ. Find the measures of the given angles or lengths of
the given sides.
5. 𝑚𝐵 = 3𝑦, 𝑚𝐺 = 𝑦 + 50
A
B
D
C
𝟑𝒚 = 𝒚 + 𝟓𝟎
𝟐𝒚 = 𝟓𝟎
𝒚 = 𝟐𝟓
F
G
𝒎𝑩 = 𝟑𝒚
𝒎𝑩 = 𝟑(𝟐𝟓)
𝒎𝑩 = 𝟕𝟓
𝒎𝑮 = 𝒚 + 𝟓𝟎
𝒎𝑮 = 𝟐𝟓 + 𝟓𝟎
J
H
𝒎𝑮 = 𝟕𝟓
Homework
Mrs. Rivas
Algebra 𝑨𝑩𝑪𝑫 𝑭𝑮𝑯𝑱. Find the measures of the given angles or lengths
of the given sides.
6. 𝐶𝐷 = 2𝑥 + 3; 𝐻𝐽 = 3𝑥 + 2
A
D
B
C
F
G
J
H
𝟐𝒙 + 𝟑 = 𝟑𝒙 + 𝟐
𝟑=𝒙+𝟐
𝟏=𝒙
𝑪𝑫 = 𝟐𝒙 + 𝟑
𝑪𝑫 = 𝟐(𝟏) + 𝟑
𝑪𝑫 = 𝟓
𝑯𝑱 = 𝟑𝒙 + 𝟐
𝑯𝑱 = 𝟑(𝟏) + 𝟐
𝑯𝑱 = 𝟓
Homework
Mrs. Rivas
Algebra 𝑨𝑩𝑪𝑫 𝑭𝑮𝑯𝑱. Find the measures of the given angles or lengths
of the given sides.
7. 𝑚𝐶 = 5𝑧 + 20, 𝑚𝐻 = 6𝑧 + 10
A
B
D
C
𝟐𝟎 = 𝒛 + 𝟏𝟎
𝒎𝑪 = 𝟓𝒛 + 𝟐𝟎
𝒎𝑪 = 𝟓 𝟏𝟎 + 𝟐𝟎
𝟏𝟎 = 𝒛
𝒎𝑪 = 𝟕𝟎
𝟓𝒛 + 𝟐𝟎 = 𝟔𝒛 + 𝟏𝟎
F
G
𝒎𝑯 = 𝟓𝒛 + 𝟐𝟎
𝒎𝑪 = 𝟓 𝟏𝟎 + 𝟐𝟎
J
H
𝒎𝑪 = 𝟕𝟎
Homework
Mrs. Rivas
Algebra 𝑨𝑩𝑪𝑫 𝑭𝑮𝑯𝑱. Find the measures of the given angles or lengths
of the given sides.
8. 𝐴𝐷 = 5𝑏 + 4; 𝐹𝐽 = 3𝑏 + 8
A
D
B
C
F
G
J
H
𝟓𝒃 + 𝟒 = 𝟑𝒃 + 𝟖
𝟐𝒃 + 𝟒 = 𝟖
𝟐𝒃 = 𝟒
𝒃=𝟐
𝑨𝑫 = 𝟓𝒃 + 𝟒
𝑨𝑫 = 𝟓(𝟐) + 𝟒
𝑨𝑫 = 𝟏𝟒
𝑭𝑱 = 𝟑𝒃 + 𝟖
𝑭𝑱 = 𝟑(𝟐) + 𝟖
𝑭𝑱 = 𝟏𝟒
Homework
Mrs. Rivas
4-2 Draw 𝑴𝑮𝑻. Use the triangle to answer the questions below.
9. What angle is included between 𝐺𝑀 and 𝑀𝑇?
G
M
∠𝑴
T
Homework
Mrs. Rivas
4-2 Draw 𝑴𝑮𝑻. Use the triangle to answer the questions below.
10. Which sides include ∠𝑇?
G
𝑻𝑮 𝒂𝒏𝒅 𝑻𝑴
M
T
Homework
Mrs. Rivas
4-2 Draw 𝑴𝑮𝑻. Use the triangle to answer the questions below.
11. What angle is included between 𝐺𝑇 and 𝑀𝐺 ?
G
M
∠𝑮
T
Mrs. Rivas
Homework
Would you use SSS or SAS to prove the triangles congruent? If there is not
enough information to prove the triangles congruent by SSS or SAS, write
not enough information. Explain your answer.
13.
12.
Not enough information;
two pairs of corresponding
sides are congruent, but
the congruent angle is not
included.
SAS;
two pairs of
corresponding sides and
their included angle are
congruent.
Homework
Mrs. Rivas
Would you use SSS or SAS to prove the triangles congruent? If there is not
enough information to prove the triangles congruent by SSS or SAS, write
not enough information. Explain your answer.
15.
14.
SSS;
three pairs of
corresponding sides
are congruent.
Not enough information;
two pairs of corresponding
sides are congruent, but
the congruent angle is not
the included angle.
Homework
Mrs. Rivas
Would you use SSS or SAS to prove the triangles congruent? If there is not
enough information to prove the triangles congruent by SSS or SAS, write
not enough information. Explain your answer.
16.
SSS;
three corresponding
sides are congruent
17.
SAS;
two pairs of corresponding
sides and their included right
angle are congruent.
Homework
Mrs. Rivas
Would you use SSS or SAS to prove the triangles congruent? If there is not
enough information to prove the triangles congruent by SSS or SAS, write
not enough information. Explain your answer.
18.
Not enough information;
one pair of corresponding sides
and corresponding angles are
congruent, but the other pair of
corresponding sides that form the
included angle must also be
congruent.
19.
SAS;
two pairs of corresponding
sides and their included vertical
angles are congruent.
Homework
Mrs. Rivas
Would you use SSS or SAS to prove the triangles congruent? If there is not
enough information to prove the triangles congruent by SSS or SAS, write
not enough information. Explain your answer.
20.
SSS or SAS;
three pairs of corresponding sides are congruent, or,
two pairs of corresponding sides and their included vertical angles are
congruent.
Mrs. Rivas
Homework
4-3 Name two triangles that are congruent by ASA.
21.
22.
∆𝑯𝑰𝑱 ≅ ∆𝑴𝑳𝑲
∆𝑹𝑺𝑻 ≅ ∆𝑿𝒀𝒁
Homework
Mrs. Rivas
23. Developing Proof Complete the proof by filling in the blanks.
Given: 𝐻𝐼𝐽 ≅ ∠𝐾𝐼𝐽, and 𝐼𝐽𝐻 ≅ ∠𝐼𝐽𝐾
Prove: 𝐻𝐼𝐽 ≅ 𝐾𝐼𝐽
Proof: 𝐻𝐼𝐽 ≅ 𝐾𝐼𝐽 and 𝐼𝐽𝐻 ≅ 𝐼𝐽𝐾 are given.
𝑪𝒐𝒏𝒈𝒓𝒖𝒆𝒏𝒕 𝑷𝒓𝒐𝒑𝒆𝒓𝒕𝒚
_____.
𝐼𝐽 ≅ 𝐼𝐽 by 𝑹𝒆𝒇𝒍𝒆𝒙𝒊𝒗𝒆
𝑨𝑺𝑨
So, 𝐻𝐼𝐽 ≅ 𝐾𝐼𝐽 by _____.
Homework
24. Given: 𝐿𝑂𝑀 ≅ 𝑁𝑃𝑀,𝐿𝑀 ≅ 𝑁𝑀
Prove: 𝐿𝑂𝑀 ≅ 𝑁𝑃𝑀
Proof: ∠𝑳𝑶𝑴 ≅ ∠𝑵𝑷𝑴 and 𝑳𝑴 ≅ 𝑵𝑴 are given.
∠𝑳𝑶𝑴 ≅ ∠𝑵𝑷𝑴 because vertical angles are ≅.
So, ∠𝑳𝑶𝑴 ≅ ∠𝑵𝑷𝑴 by AAS.
Mrs. Rivas