Download Proving Angles Congruent

Congruent Angles Continued
GEOMETRY (HOLT 2-7—PART OF) K. SANTOS
Vertical Angles Theorem (2-7-2)
Vertical angles are congruent
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<1≅<3
< 2 ≅ <4
Example 1—Vertical Angles
If a = 70°, then find x, y and z.
Since a and y are vertical
Angles they are congruent.
So, y = 70°.
a x
z y
a and x are a linear pair, so
They add to 180° and are
Supplementary. So,
180 - 70 =110°.
x and z are vertical angles
So they are congruent also.
So z = 110°.
Example 2—Vertical Angles
Find the value of x.
2x + 3
4x - 101
4x – 101 = 2x + 3
2x – 101 = 3
2x = 104
x = 52°
Theorem (2-7-3)
If two congruent angles are supplementary then each
angle is a right angle.
Given: < 1 ≅ < 2
< 1 and < 2 supplementary
Then: <1 and < 2 are right angles
If m< 1 =x then m< 2= x.
So: x + x = 180°
2x = 180°
x= 90° which means it is a right angle
Since x is <1, then < 1 is a right angle
And since <1 ≅ <2, then < 2 is a right angles
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