HomeworkMrs. Rivas
4-1 . List each of the following.
1. three pairs of congruent sides
2. three pairs of congruent angles
๐ช๐จโ ๐ฑ๐บ๐จ๐ป โ ๐บ๐ซ๐ช๐ป โ ๐ฑ๐ซ
โ ๐ชโ โ ๐ฑโ ๐จโ โ ๐บโ ๐ป โ โ ๐ซ
HomeworkMrs. Rivas
Algebra Find the values of the variables.
3.
๐ ๐ ๐๐
๐ ๐+๐๐+๐ ๐+๐=๐๐๐๐ ๐+๐๐=๐๐๐
๐ ๐=๐๐๐๐=๐๐
HomeworkMrs. Rivas
Algebra Find the values of the variables.
4.
๐ ๐=๐๐๐=๐
HomeworkMrs. Rivas
Algebra ABCD FGHJ. Find the measures of the given angles or lengths of the given sides.
5.
A B
CD
F G
HJ
๐ ๐=๐+๐๐๐ ๐=๐๐
๐=๐๐
๐๐ฉ=๐ ๐๐๐ฉ=๐(๐๐)๐๐ฉ=๐๐
๐๐ฎ=๐+๐๐๐๐ฎ=๐๐+๐๐๐๐ฎ=๐๐
HomeworkMrs. Rivas
Algebra . Find the measures of the given angles or lengths of the given sides.
6.
A B
CD
F G
HJ
๐ ๐+๐=๐ ๐+๐๐=๐+๐๐=๐
๐ช๐ซ=๐ ๐+๐๐ช๐ซ=๐(๐)+๐๐ช๐ซ=๐
๐ฏ๐ฑ=๐ ๐+๐๐ฏ๐ฑ=๐ (๐)+๐๐ฏ๐ฑ=๐
HomeworkMrs. Rivas
Algebra . Find the measures of the given angles or lengths of the given sides.
7.
A B
CD
F G
HJ
๐ ๐+๐๐=๐ ๐+๐๐๐๐=๐+๐๐๐๐=๐
๐๐ช=๐ ๐+๐๐๐๐ช=๐ (๐๐ )+๐๐๐๐ช=๐๐
๐๐ฏ=๐ ๐+๐๐๐๐ช=๐ (๐๐ )+๐๐๐๐ช=๐๐
HomeworkMrs. Rivas
Algebra . Find the measures of the given angles or lengths of the given sides.
8.
A B
CD
F G
HJ
๐๐+๐=๐๐+๐๐๐+๐=๐
๐๐=๐๐=๐
๐จ๐ซ=๐๐+๐๐จ๐ซ=๐(๐)+๐๐จ๐ซ=๐๐
๐ญ ๐ฑ=๐๐+๐๐ญ ๐ฑ=๐ (๐)+๐๐ญ ๐ฑ=๐๐
HomeworkMrs. Rivas
4-2 Draw . Use the triangle to answer the questions below.
9. What angle is included between and ?
M
G
T
โ ๐ด
HomeworkMrs. Rivas
4-2 Draw . Use the triangle to answer the questions below.10. Which sides include ?
M
G
T
๐ป๐ฎ๐๐๐ ๐ป๐ด
HomeworkMrs. Rivas
4-2 Draw . Use the triangle to answer the questions below.
11. What angle is included between and ?
M
G
T
โ ๐ฎ
HomeworkMrs. 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.
12. 13.
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.
HomeworkMrs. 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.
14. 15.
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.
HomeworkMrs. 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. 17.
SSS; three corresponding sides are congruent
SAS; two pairs of corresponding sides and their included right angle are congruent.
HomeworkMrs. 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. 19.
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.
SAS; two pairs of corresponding sides and their included vertical angles are congruent.
HomeworkMrs. 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.
HomeworkMrs. Rivas
4-3 Name two triangles that are congruent by ASA.
21. 22.
โ ๐ฏ๐ฐ๐ฑ โ โ๐ด๐ณ๐ฒ โ ๐น๐บ๐ป โ โ๐ฟ๐๐
HomeworkMrs. Rivas
23. Developing Proof Complete the proof by filling in the blanks. Given: , and
Prove:
Proof: and are given.
๐ผ๐ฝ โ ๐ผ๐ฝ by _____.
So, by _____.
๐น๐๐๐๐๐๐๐๐ ๐ช๐๐๐๐๐๐๐๐ ๐ท๐๐๐๐๐๐๐
๐จ๐บ๐จ
HomeworkMrs. Rivas
24. Given: ,
Prove:
Proof: and are given.
So, by AAS.
because vertical angles are .
HomeworkMrs. Rivas
(4-4) 1. Complete the proof.
Given: , ,
Prove:
Statements Reasons
a) , a)
b) and are right angles. b) Definition of right angles
c) c)
d) d) Vertical angles are congruent.
e) e)
f) f)
g) g)
Given
All right angles are congruentโ ๐ฌ๐ช๐ซโ โ ๐จ๐ช๐ฉGivenโ๐ช๐ซ๐ฌ โ โ๐ช๐ฉ๐จ ASA
CPCTC
HomeworkMrs. Rivas
(4-5) Algebra Find the values of and .2.
๐๐๐โ๐๐๐=๐๐๐๐๐๐
๐=๐๐
๐น๐๐๐๐๐๐๐๐๐๐๐๐+๐๐=๐๐๐๐=๐๐
base angles are congruent
HomeworkMrs. Rivas
Algebra Find the values of and .
3. all sides are equal and all angles are
equal
๐๐๐+๐=๐๐ ๐ โ๐๐=๐๐๐=๐๐ ๐=๐๐๐๐
๐๐
HomeworkMrs. Rivas
Algebra Find the values of and .
4.
๐น๐๐๐๐๐๐๐๐๐๐๐๐+๐๐=๐๐๐
๐=๐๐
๐+๐๐๐=๐๐๐๐=๐๐
HomeworkMrs. Rivas
Algebra Find the values of and .
5.
base angles are congruent
๐๐+๐๐+๐=๐๐๐๐๐+๐=๐๐๐๐=๐๐
๐+๐+๐๐๐=๐๐๐๐ ๐+๐๐๐=๐๐๐
๐ ๐=๐๐๐=๐๐
HomeworkMrs. Rivas
(4-5) Algebra Find the values of and .6.
all sides are equal and all angles are equal๐ ๐=๐๐
๐=๐๐๐น๐๐๐๐๐๐๐๐๐๐๐๐=๐๐+๐๐๐=๐๐๐
๐๐
๐๐ ๐๐
HomeworkMrs. Rivas
(4-5) Algebra Find the values of and .7.
base angles are congruent
๐๐ ๐๐ ๐=๐๐
๐๐
๐๐+๐๐+๐+๐๐=๐๐๐๐๐๐+๐=๐๐๐
๐=๐๐
HomeworkMrs. Rivas
Use the properties of isosceles and equilateral triangles to find the measure of the indicated angle.
8.
๐๐
๐๐+๐โ ๐จ๐ช๐ฉ=๐๐๐๐โ ๐จ๐ช๐ฉ=๐๐๐
HomeworkMrs. Rivas
Use the properties of isosceles and equilateral triangles to find the measure of the indicated angle.
9.
๐๐
๐๐+๐๐+๐โ ๐ซ๐ฉ๐ช=๐๐๐๐๐๐+๐โ ๐ซ๐ฉ๐ช=๐๐๐
๐โ ๐ซ๐ฉ๐ช=๐๐
HomeworkMrs. Rivas
Use the properties of isosceles and equilateral triangles to find the measure of the indicated angle.
10.
๐๐
๐๐+๐๐+๐โ ๐ซ๐ช๐ฌ=๐๐๐๐๐๐+๐โ ๐ซ๐ช๐ฌ=๐๐๐
๐โ ๐ซ๐ช๐ฌ=๐๐๐๐
๐๐๐๐ ๐๐
๐โ ๐จ๐ฉ๐ช=๐๐
HomeworkMrs. Rivas
Algebra Find the values of m and n.
11.
๐๐
๐=๐๐
(๐+๐๐)+(๐+๐๐)+๐๐=๐๐๐๐๐+๐๐+๐๐=๐๐๐๐๐+๐๐๐=๐๐๐
๐๐=๐๐๐=๐๐
HomeworkMrs. Rivas
Algebra Find the values of m and n.
12.
๐๐
๐๐+๐๐+?=๐๐๐? ๐๐๐+?=๐๐๐
?=๐๐๐๐
๐๐
๐=๐๐
๐=๐๐
HomeworkMrs. Rivas
Algebra Find the values of m and n.
13.
base angles are congruent
๐+๐+๐๐=๐๐๐๐๐+๐๐=๐๐๐
๐๐=๐๐๐=๐๐
๐๐
๐๐๐๐
๐+๐+๐๐=๐๐๐๐๐+๐๐=๐๐๐
๐๐=๐๐๐๐=๐๐ .๐
HomeworkMrs. Rivas
(4-6) Algebra For what values of x or x and y are the triangles congruent by HL?
14.
๐ ๐+๐=๐๐๐ ๐=๐๐๐=๐
๐ ๐+๐=๐ ๐โ๐ ๐๐(๐)+๐=๐(๐)โ๐ ๐๐+๐=๐๐โ๐๐๐+๐ ๐=๐๐
๐ ๐=๐๐๐=๐
HomeworkMrs. Rivas
(4-6) Algebra For what values of or and are the triangles congruent by ?
15.
๐ ๐+๐=๐+๐๐+๐=๐๐=๐
๐+๐=๐๐ โ๐ ๐(๐ )+๐=๐ (๐ ) โ๐ ๐๐+๐=๐โ๐ ๐๐+๐ ๐=๐๐ ๐=๐๐=๐
HomeworkMrs. Rivas
(4-6) Algebra For what values of or and are the triangles congruent by ?
16.
๐+๐=๐+๐๐=๐
๐+๐=๐ ๐ โ๐๐+๐=๐(๐)โ๐๐๐=๐๐โ ๐๐=๐
HomeworkMrs. Rivas
17. Developing Proof Complete the paragraph proof.
Given:
Prove:
Proof: It is given that . So, _____ and _______are _______ angles
because perpendicular lines form ______ angles. _______ by the
Reflexive Property of Congruence. It is given that _______. So,
by _______.
โ ๐น๐ป๐บ โ ๐น๐ป๐ผ ๐๐๐๐๐
๐๐๐๐๐ ๐น๐ป
๐น๐ผ๐ฏ๐ณ
HomeworkMrs. Rivas
(4-7) Separate and redraw the indicated triangles. Identify any common angles or sides.
16. โ๐ต๐๐ดโงโ๐ถ๐๐ด
โ ๐จ
HomeworkMrs. Rivas
(4-7) Separate and redraw the indicated triangles. Identify any common angles or sides.
17. โ๐บ๐ธ๐ปโงโ๐น๐ธ๐ป
๐ฌ๐ฏ
HomeworkMrs. Rivas
(4-7) Separate and redraw the indicated triangles. Identify any common angles or sides.
18. โ๐๐๐โงโ๐๐๐
๐ต๐๐๐