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Right Angle Theorem Application in Geometric Proofs

Learn how to prove angles are right angles using the Right Angle Theorem in this comprehensive lesson. Explore various scenarios and geometric properties to enhance your understanding.

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Right Angle Theorem Application in Geometric Proofs

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  1. Right Angle Theorem Lesson 4.3

  2. 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.

  3. Paragraph Proof: Since 1 and 2 form a straight angle, they are supplementary.Therefore, m1 + m2 = 180°. Since 1 and 2 are congruent, we can use substitution to get the equation: m1 + m2 = 180° or m1 = 90°. Thus, 1 is a right angle and so is 2.

  4. 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

  5. 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

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