Download Section 4.3-A Right Angle Theorem

Section 4.3-A Right
Angle Theorem
By Scott Salmon and J.C.
Show
Theorem # 23

If two angles are both
supplementary and
congruent, then they
are right angles.
WHAT????

Since angle 1 and angle 2 form a straight
angle, they are supplementary. Therefore,
angle 1 plus angle 2 equals 180 degrees.
Sample Problem#1
C
Given: CA congruent CB
AQ congruent QB
Prove: angle
AQC and angle
BQC are right
angles
A
B
Q
Answer
Statements
1: CA congruent CB
2: AQ congruent QB
3: Angle AQC is suppl. to
angle BQC
4: Angles AQC and BQC are
right angles
Reasons
1: Given
2: Given
3: If 2 adj. angles form a straight
angle( Assumed from diagram), then
the angles are suppl.
4: If 2 angles are both suppl. and
congruent, then they are right angles
Sample Problem #2
Z
W
Given:
Triangles SZT
and AZT are
congruent
S
Prove: Angles
STZ and ATZ
are right
angles
T
A
Q
Answer
Statements
1: Triangles SZT and AZT are
congruent
2: Angle STZ is congruent to
angle AZT
3:Angle STZ is suppl. to
angle AZT
4:Angle STZ and Angle AZT
are right angles
Reasons
1: Given
2: CPCTC
3: IF two adj. angles form a
straight angle, then they are suppl.
4: If two angles are both suppl.
and congruent, then they are right
angles
Practice Problem #1
D
65
Given: Angle ADB is
compl. to BDC and
Angle ABD
is congruent to angle
DBC
Find : Measures of
ALL angles
A
B
C
Answer
D
65
(35)
(65)
A
(90)
(90)
B
(35)
Explanation: Angle ADB
is 35 degrees
(subtraction),
ABD is suppl. To CBD
(Assumed from
diagram)
Therefore, angles ABD
and CBD are right
angles (theorem 23),
Angle BCD is 35
C
degrees (subtraction)
and angle BAD is 65
degrees (subtraction)
Practice Problem #2
T
Y
P
Given: Angle
TPY
is congruent to
Angle OPY,
Angle TPY is
suppl. To angle
OPY
R
Prove: TYOR is
a rhombus
O
Answer
Statements
1: Angle TPY
is congruent to Angle OPY
2: Angle TPY is suppl. to
Angle OPY
3. Angle TPY and OPY are
right angles
4: Angle RPT is congruent
to OPY, and Angle RPO is
congruent to Angle YPT
5:TYOR is a rhombus
Reasons
1: Given
2: Given
3: Theorem 23 (a right angle
theorem)
4: Vertical angles are congruent
5: If a quad’s diagonals are
perpendicular, then the quad is a
rhombus
Works Cited

Rhoad, Richard, George Milauskas, and
Robert Whipple. Geometry for
Enjoyment and Challenge. Evanston,
IL: McDougal, Littell, 1991. Print.
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