question

R, S, and T are the vertices of one triangles. E, F, and F are the vertices of another triangles. mâˆ R = 60, mâˆ S = 80, mâˆ F = 60, mâˆ D = 40, RS = 4, and EF = 4. Are the two triangles congruent? If yes, explain and tell which segment is congruent to lines RT.

answer

A. yes, by ASA; line FD

question

Find the value of x. The diagram is not to scale.
Given: RS â‰… ST, mâˆ RST = 7x - 54, mâˆ STU = 8x.

answer

A. 14

question

What additional information will allow you to prove the triangles congruent by the HL Theorem?

answer

C. AC â‰… DC

question

All equilateral triangles are also isosceles.

answer

A. True

question

In an isosceles triangle with two congruent sides, the angles across from the legs are called ____ angles.

answer

base

question

Supply the missing reasons to complete the proof.
3. Î”PRQ â‰… Î”SRT
3. _____
4. PR â‰… SR
4. _____

answer

3. Angle-Side-Angle (ASA) Postulate, 4. CPCTC

question

Complete the proof by providing the missing statement and reasons.
2. âˆ SDH and âˆ SDT are right âˆ s.
2. ____
3 SH â‰… ST
3. ____
4. ____
4. Reflexive Property
5. Î”SHD â‰… Î”STD
5. ____

answer

2. Definition of perpendicular angles, 3. Given, 4. SD is congruent to SD *OR* SD is congruent to DS, 5. Hypotenuse-Leg (HL) Theorem.

question

How are the angles of an equilateral triangle related?

answer

All three sides being equal length to each other.

question

How does the length of the hypotenuse in a right triangle compare to the lengths of the legs?

answer

Hypotenuse is greater in length. Pythagorean theorem states a^2 + b^2 = c^2, so the legs should add up to the hypotenuse.

question

Explain how proving two triangles congruent can help prove parts of the triangle congruent.

answer

By CPCTC, since you can identify the corresponding angles and sides of one triangle to the other/ Corresponding parts of congruent triangles are congruent.