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## Right Angle Theorem

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**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:**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 P Prove: PS QR Τ S Q R • Circle P • Draw PQ and PR • PQ PR • S mdpt QR • QS RS • PS PS • PSQ PSR • PSQ PSR • PSQ & PSR are supp. • PSQ and PSR are rt s • PS QR • Given • Two points determine a seg. • Radii of a circle are . • Given • A mdpt divides a segment into 2 segs. • Reflexive property. • SSS • CPCTC • 2 s that make a straight are supp. • If 2 s are both supp and , they are rt s. • If 2 lines intersect to form rt s, they are . Τ Τ**Given: ABCD is a rhombus**AB BC CD AD Prove: AC BD A D 5 4 7 2 E 1 Τ 3 6 8 B C Hint: Draw and label shape! • Given • Reflexive Property • SSS • CPCTC • If then • ASA • CPCTC • 2 s that make a straight are supp. • If 2 s are both supp and they are rt s. • If 2 lines intersect and form rt s, they are . • AB BC CD AD • AC AC • BAC DAC • 7 5 • 3 4 • ABE ADE • 1 2 • 1 & 2 are supp. • 1 and 2 are rt s • AC BD Τ Τ