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.
answer
A. yes, by ASA; line FD
question
Find the value of x. The diagram is not to scale.
Given: RS ≅ ST, m∠RST = 7x - 54, m∠STU = 8x.
answer
A. 14
question
What additional information will allow you to prove the triangles congruent by the HL Theorem?
answer
C. AC ≅ 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. ΔPRQ ≅ ΔSRT
3. _____
4. PR ≅ SR
4. _____
answer
3. Angle-Side-Angle (ASA) Postulate, 4. CPCTC
question
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. ____
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.
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