Activity 1
Note: This question asks for corresponding parts, not congruence statements. Instead of using
congruent signs, use the “goes to” arrow notation we learned about during our study of
transformations.
̅̅̅̅
̅̅̅ → 𝑇𝑂
a. 𝐹 → 𝑇
b.
𝐹𝐼
c.
∠𝐹 → ∠𝑇
̅̅̅̅
̅̅̅ → 𝑂𝑃
𝐼→𝑂
𝐼𝑋
∠𝐼 → ∠𝑂
̅̅̅̅
̅̅̅̅
𝑿→𝑃
𝐹𝑋 → 𝑇𝑃
∠𝑋 → ∠𝑃
d.
Yes, since the corresponding parts are still in the correct position, this is a valid congruence
statement for the two triangles.
e.
No, since I corresponds with T, and those vertices are not in corresponding positions in the
congruence statement, this is not a valid congruence statement for the two triangles.
Activity 2
2.
𝑀𝑁 ≅ 𝑈𝑉, 𝑁𝑃 ≅ 𝑉𝑊, 𝑀𝑃 ≅ 𝑈𝑊, ∠𝑀 ≅ ∠𝑈, ∠𝑁 ≅ ∠𝑉, ∠𝑃 ≅ ∠𝑊
3.
By corresponding parts, MN = UV = 14 cm and 𝑚∠𝑈 = 𝑚∠𝑀 = 24°
4.
By corresponding parts, VW = PN = 8 inches
It is given that MN = 2PN ------- This is saying two times the length of PN
By substitution, MN= 2(8) = 16 inches
Activity 3
7.
This questions asks for the measure of an angle. We know from the Triangle Sum Theorem that
the sum of the angles in a triangle is equal to 180 degrees. We can use that theorem to develop an
equation, similar to what we did using the definition of supplementary angles or the angle addition
postulate, as follows:
𝑚∠𝑀 + 𝑚∠𝑁 + 𝑚∠) = 180
By corresponding parts, we know that 𝑚∠𝑃 = 𝑚∠𝑀 = 64°, so we can use substitution
64 + 57 + (5𝑥 + 4) = 180
By combining like terms, we get x=11
We can use substitution again to solve for 𝑚∠𝑅 = 𝑚∠𝑂 = 5𝑥 + 4 = 5(11) + 4 = 59
45.
This question is done in an almost identical fashion, resulting in x = 11
Activity 4
32.
a.
b.
c.
d.
34.
D
36.
a.
b.
c.
d.
PC
∠𝐶𝑃𝐵
∠𝑃𝐴𝐵
∆𝑃𝐵𝐶
AAS
ASA
SAS
SSS
Activity 5
37.
a.
b.
c.
d.
∠𝐶 ≅ ∠𝐹
∠𝐹 ≅ ∠𝐵 𝑜𝑟 ∠𝐸 ≅ ∠𝐶 𝑜𝑟 ∠𝐹 ≅ ∠𝐶 𝑜𝑟 ∠𝐸 ≅ ∠𝐵
𝐵𝐶 ≅ 𝐸𝐹 𝑎𝑛𝑑 𝐴𝐶 ≅ 𝐷𝐹
𝐴𝐵 ≅ 𝐷𝐸
38.
This problem asks, based on the given information in each answer choice, can you determine if
the triangles are congruent. You should treat each answer choice independently of one another.
Marking the diagram with information from choice A makes the triangles congruent using ASA, choice B
uses AAS, choice C uses SAS. Choice D could be SSA, but since the triangles are not right triangles, we
cannot use this criteria (which we would otherwise called HL in a right triangle), as it represents an
ambiguous case (the triangles may or may NOT be congruent).
43.
B
Activity 6
42.
a.
b.
c.
d.
Congruent angles were bisected, so the resulting pieces are also congruent.
DCB
BC
ASA
40.
(4, 5)
48.
B
50.
a.
b.
SRP
It is the perpendicular bisector of QR
Activity 7
39.
Yes, since an obtuse triangle can also be isosceles.
47.
a.
b.
c.
d.
Yes, since they have right angles.
BC=13, YZ=13
AB=5, XY=5
Yes, using the HL criteria