Question

given triangle ghi with sides gh = 4 cm, hi = 6 cm, and gi = 8 cm, what is required for triangle jkl to be congruent to triangle ghi by sss?
a. jkl must have one equal side and two equal angles to ghi.
b. jkl must have sides jk = 4 cm, kl = 6 cm, and jl = 8 cm.
c. jkl must have two equal sides and one equal angle to ghi.
d. jkl must have all three angles equal to ghi.

which of the following properties is always true for triangles proven congruent by sss?
a. their altitudes are equal.
b. their perimeters are equal.
c. their corresponding sides and angles are equal.
d. their medians are equal.

triangle xyz has sides xy = 3, yz = 5, and xz = 6. which set of side lengths ensures triangle abc is congruent to triangle xyz by sss?
a. ab = 5, bc = 6, ac = 4
b. ab = 3, bc = 5, ac = 6
c. ab = 6, bc = 3, ac = 5
d. ab = 3, bc = 6, ac = 5

Explanation:

Step1: Recall SSS congruence rule

The SSS (Side - Side - Side) congruence rule states that two triangles are congruent if their corresponding sides are equal.

Step2: Solve first question

For $\triangle JKL$ to be congruent to $\triangle GHI$ by SSS, the corresponding sides must be equal. Given $GH = 4$ cm, $HI=6$ cm, $GI = 8$ cm, then $JK = 4$ cm, $KL = 6$ cm, and $JL = 8$ cm. So the answer to the first question is b.

Step3: Solve second question

If two triangles are congruent by SSS, then their corresponding sides and angles are equal. While altitudes, perimeters and medians may be equal for congruent triangles, the most fundamental and always - true property for SSS - congruent triangles is that corresponding sides and angles are equal. So the answer to the second question is c.

Step4: Solve third question

For $\triangle ABC$ to be congruent to $\triangle XYZ$ by SSS, with $XY = 3$, $YZ = 5$, and $XZ = 6$, we need $AB = 3$, $BC = 5$, and $AC = 6$. So the answer to the third question is b.

Answer:

1. b. JKL must have sides JK = 4 cm, KL = 6 cm, and JL = 8 cm.
2. c. Their corresponding sides and angles are equal.
3. b. AB = 3, BC = 5, AC = 6