Right Angle Theorem. Lesson 4.3. Theorem 23: If two angles are both supplementary and congruent, then they are right angles. 2. 1. Given: 1 2 Prove: 1 and 2 are right angles. Paragraph Proof:.
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Theorem 23:If two angles are both supplementary and congruent, then they are right angles.
Given: 1 2
Prove: 1 and 2 are right angles.
Since 1 and 2 form a straight angle, they are supplementary.Therefore, m1 + m2 = 180°.
Since 1 and 2 are congruent, we can use substitution to get the equation:
m1 + m2 = 180° or m1 = 90°.
Thus, 1 is a right angle and so is 2.
Given: Circle P
S is the midpoint of QR
Prove: PS QR
AB BC CD AD
Prove: AC BD
Hint: Draw and label shape!