GEOM A, U5L6: Congruence in Right Triangles Quiz PART 1

Find the value of x. The diagram is not to scale. Given: RS ≅ ST, m∠RST = 7x - 54, m∠STU = 8x.

A. 14

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

base

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

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

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

C. AC ≅ DC

Complete the proof by providing the missing statement and reasons. 2. ∠SDH and ∠SDT are right ∠s. 2. ____ 3 SH ≅ ST 3. ____ 4. ____ 4. Reflexive Property 5. ΔSHD ≅ ΔSTD 5. ____

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

Supply the missing reasons to complete the proof. 3. ΔPRQ ≅ ΔSRT 3. _____ 4. PR ≅ SR 4. _____

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

All equilateral triangles are also isosceles.

A. True

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

A. yes, by ASA; line FD

How are the angles of an equilateral triangle related?

All three sides being equal length to each other.

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

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