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## PowerPoint Slideshow about ' Right Angle Theorem' - arama

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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.

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

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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