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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:.

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slide2

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.

slide3

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.

slide4

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

slide5

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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