Question

if triangle mno and triangle pqr are congruent by sss criterion, and mn = 3y + 2, pq = 14, what is the value of y?
a. 3
b. 4
c. 5
d. 2

a triangle has sides 5 cm, 7 cm, and 10 cm. which of the following cannot form a triangle congruent to it by sss?
a. 6 cm, 7 cm, 10 cm
b. 7 cm, 5 cm, 10 cm
c. 5 cm, 7 cm, 10 cm
d. 10 cm, 7 cm, 5 cm

given two triangles are congruent, what can be said about their corresponding angles?
a. they are supplementary
b. they are equal
c. they are right angles
d. they are complementary

Explanation:

Step1: Set up equation from congruence

Since $\triangle MNO$ and $\triangle PQR$ are congruent by SSS and $MN = 3y + 2$, $PQ=14$, we have $3y + 2=14$.

Step2: Solve for y

Subtract 2 from both sides: $3y=14 - 2=12$. Then divide both sides by 3: $y=\frac{12}{3}=4$.

For the second - question:
By the SSS (Side - Side - Side) congruence criterion, two triangles are congruent if their corresponding sides are equal. A triangle with side lengths 5 cm, 7 cm, and 10 cm will be congruent to another triangle with the same side lengths regardless of the order. Option a has side lengths 6 cm, 7 cm, 10 cm which cannot form a triangle congruent to the given triangle by SSS.

For the third - question:
If two triangles are congruent, then their corresponding angles are equal. This is a fundamental property of congruent triangles.

Answer:

1. b. 4
2. a. 6 cm, 7 cm, 10 cm
3. b. They are equal