Practice Problems
a) 𝑎 = 40°
b) 𝑎 = 80°
c) 𝑎 = 90°
d) 𝑎 = 140°
a) 𝑥 = 50°
b) 𝑥 = 80°
c) 𝑥 = 100°
d) 𝑥 = 130°
If ∆𝐶𝐸𝐷~∆𝐾𝐻𝐺 …
a) 𝑥 = 90°
b) 𝑥 = 64°
c) 𝑥 = 26°
d) 𝑥 = 116°
a) 𝑥 = 3
b) 𝑥 = 6
c) 𝑥 = 12
d) 𝑥 = 30
a) The triangles are similar by SSS
b) The triangles are similar by SAS
c) The triangles are similar by AA
d) There is not enough information to determine
a) The triangles are similar by SSS
b) The triangles are similar by SAS
c) The triangles are similar by AA
d) There is not enough information to determine
a) The triangles are similar by SSS
b) The triangles are similar by SAS
c) The triangles are similar by AA
d) There is not enough information to determine
What further information do you need in order to
determine the triangles are similar by SAS?
What further information do you need in order to
determine the triangles are similar by SAS?
a)
20
15
=
𝑀𝑇
𝐾𝐵
b) 𝑚∠𝑇 = 𝑚∠𝐵
c)
20
15
=
𝐴𝑇
𝐻𝐵
d) 𝑚∠𝑀 = 𝑚∠𝐾
In the figure below, ∠1 = 4𝑥° and ∠7 = 76°
In the figure below, ∠1 = 4𝑥° and ∠7 = 76°
a) 𝑥 = 18
b) 𝑥 = 19
c) 𝑥 = 26
d) 𝑥 = 100
In the figure below,
∠3 = (4𝑥 + 17)° and ∠6 = (6𝑥 − 13)°
In the figure below,
∠3 = (4𝑥 + 17)° and ∠6 = (6𝑥 − 13)°
a) 𝑚∠2 = 15°
b) 𝑚∠2 = 60°
c) 𝑚∠2 = 77°
d) 𝑚∠2 = 180°
Prove that ∆𝐴𝐵𝐶~∆𝐷𝐸𝐹.
Given: 𝐴𝐵 = 8, 𝐵𝐶 = 12,
𝐴𝐶 = 16, 𝐷𝐸 = 6, 𝐸𝐹 = 9, 𝐷𝐹 = 12
Given: 𝐴𝐵 = 8, 𝐵𝐶 = 12,
𝐴𝐶 = 16, 𝐷𝐸 = 6, 𝐸𝐹 = 9, 𝐷𝐹 = 12
Sides are
proportional
𝐴𝐵 𝐵𝐶 𝐶𝐴
=
=
𝐷𝐸 𝐸𝐹 𝐹𝐷
Sides are
proportional
𝐴𝐵 𝐵𝐶 𝐶𝐴
=
=
𝐸𝐹 𝐷𝐸 𝐹𝐷
SSS
∆𝐴𝐵𝐶~∆𝐷𝐸𝐹
SSS
∆𝐴𝐵𝐶~∆𝐷𝐸𝐹
Prove that ∆𝐴𝐵𝐶~∆𝐷𝐸𝐹.
Given: 𝐴𝐵 = 8, 𝐵𝐶 = 12,
𝐴𝐶 = 16, 𝐷𝐸 = 6, 𝐸𝐹 = 9, 𝐷𝐹 = 12
Given: 𝐴𝐵 = 8, 𝐵𝐶 = 12,
𝐴𝐶 = 16, 𝐷𝐸 = 6, 𝐸𝐹 = 9, 𝐷𝐹 = 12
Sides are
proportional
𝐴𝐵 𝐵𝐶 𝐶𝐴
=
=
𝐷𝐸 𝐸𝐹 𝐹𝐷
Sides are
proportional
𝐴𝐵 𝐵𝐶 𝐶𝐴
=
=
𝐸𝐹 𝐷𝐸 𝐹𝐷
SSS
∆𝐴𝐵𝐶~∆𝐷𝐸𝐹
SSS
∆𝐴𝐵𝐶~∆𝐷𝐸𝐹
Prove that ∆𝐴𝐵𝐸~∆𝐴𝐶𝐷.
Given: 𝑚∠𝐴𝐵𝐸 = 52, 𝑚∠𝐵𝐶𝐷 = 52
∠𝐴𝐵𝐸 ≅ ∠𝐵𝐶𝐷
∠𝐴 ≅ ∠𝐴
∆𝐴𝐵𝐸~∆𝐴𝐶𝐷
Prove that ∆𝐴𝐵𝐸~∆𝐴𝐶𝐷.
Given: 𝑚∠𝐴𝐵𝐸 = 52, 𝑚∠𝐵𝐶𝐷 = 52
Definition of
Congruent
∠𝐴𝐵𝐸 ≅ ∠𝐵𝐶𝐷
Reflexive
Property
∠𝐴 ≅ ∠𝐴
AA
∆𝐴𝐵𝐸~∆𝐴𝐶𝐷
Prove that∠5 & ∠3
are supplementary.
Given: 𝑙∥𝑚