Question

match the letter of the property, definition, postulate, or theorem that justifies each statement. if m<abc = 90, then <abc is a right angle. supplement theorem if m<3 + m<4 = 180, then <3 and <4 are supplementary angles choose if m<pqr = m<rst, then <pqr ≅ <rst choose if <1 and <2 form a right angle, then <1 and <2 are complementary angles choose if <x and <y are supplementary and <x and <z are supplementary, then <y ≅ <z choose if <j and <k are vertical angles, then <j ≅ <k choose if <pqr and <stu are choose

Explanation:

1. By definition, an angle with a measure of 90 degrees is a right - angle. The first statement uses the definition of a right - angle.
2. By definition, two angles whose sum of measures is 180 degrees are supplementary angles.
3. If the measures of two angles are equal, then the angles are congruent by the definition of congruent angles.
4. If two angles form a right - angle (sum of measures is 90 degrees), they are complementary by the definition of complementary angles.
5. If two angles are supplementary to the same angle, then they are congruent. This is the Congruent Supplements Theorem.
6. Vertical angles are congruent by the Vertical Angles Theorem.

Answer:

1. Definition of a right - angle
2. Definition of supplementary angles
3. Definition of congruent angles
4. Definition of complementary angles
5. Congruent Supplements Theorem
6. Vertical Angles Theorem