Right Angle Theorem

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# Right Angle Theorem - PowerPoint PPT Presentation

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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### 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, 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.

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