Right Angle Theorem

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
?
S
Q
R

1. Circle P
2. Draw PQ and PR
3. PQ ? PR
4. S mdpt QR
5. QS ? RS
6. PS ? PS
7. PSQ ? PSR
8. ?PSQ ? ?PSR
9. ?QSR is a straight ?
10. ?PSQ ?PSR are supp.
11. ?PSQ and ?PSR are rt ?s
12. PS QR

1. Given
2. Two points determine a seg.
3. Radii of a circle are ? .
4. Given
5. A mdpt divides a segment into 2 ? segs.
6. Reflexive property.
7. SSS
8. CPCTC
9. Assumed from diagram.
10. 2 ?s that make a straight ? are supp.
11. If 2 ?s are both supp and ?, they are rt ?s.
12. If 2 lines intersect to form rt ?s, they are .

?
?
5
Given ABCD is a rhombus AB ? BC ? CD ?
AD Prove AC BD
A
D
5
4
7
2
E
1
?
6
3
8
B
C
Hint Draw and label shape!

1. Given
2. Reflexive Property
3. SSS
4. CPCTC
5. If then
6. ASA
7. CPCTC
8. Assumed from diagram.
9. 2 ?s that make a straight ? are supp.
10. If 2 ?s are both supp and ? they are rt ?s.
11. If 2 lines intersect and form rt ?s, they are .

1. AB ? BC ? CD ? AD
2. AC ? AC
3. BAC ? DAC
4. ?7 ? ?5
5. ?3 ? ?4
6. ABE ? ADE
7. ?1 ? ?2
8. ?BED is a straight ?
9. ?1 ?2 are supp.
10. ?1 and ?2 are rt ?s
11. AC BD

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