congruence in right triangles quiz part 1
1. Which of the following statements is true about congruence in right triangles?
a. Two right triangles are congruent if their corresponding angles are equal.
b. Two right triangles are congruent if their corresponding sides are equal.
c. Two right triangles are congruent if their hypotenuses are equal.
d. Two right triangles are congruent if their corresponding angles and sides are equal.
Answer: d. Two right triangles are congruent if their corresponding angles and sides are equal.
2. In a right triangle, which of the following angles is always equal to 90 degrees?
a. Acute angle
b. Obtuse angle
c. Hypotenuse
d. None of the above
Answer: d. None of the above. In a right triangle, the right angle specifically measures 90 degrees.
3. If two right triangles have congruent hypotenuses, which of the following statements is true?
a. The triangles are congruent.
b. The triangles are similar.
c. The triangles are not necessarily congruent or similar.
d. The triangles are always similar, but not necessarily congruent.
Answer: c. The triangles are not necessarily congruent or similar. Congruent hypotenuses alone do not guarantee congruence or similarity of the entire triangles.
4. Which of the following congruence criteria is specific to right triangles?
a. SAS
b. ASA
c. SSS
d. none of the above
Answer: d. None of the above. Right triangles also follow the congruence criteria of SAS and ASA, in addition to the general SSS criteria.
5. If two right triangles have equal leg lengths, what can be concluded about their hypotenuses?
a. The hypotenuses are equal in length.
b. The hypotenuses are not equal in length.
c. The hypotenuses may or may not be equal in length.
d. No conclusion can be drawn about the hypotenuses.
Answer: c. The hypotenuses may or may not be equal in length. Equal leg lengths do not guarantee that the hypotenuses of the triangles are also equal.