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Honors GeometryIsosceles Triangles
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LegLeg
BaseAngles
Base
Remember– the properties of an isosceles triangle…..
Vertex Angle
Vertex Angle
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Investigating Isosceles TrianglesUse a straightedge to draw an
ACUTE ISOSCELES triangle-- where and is the acute vertex angle.
Use scissors to cut the triangle outThen fold the triangle as shownREPEAT the procedure for an
OBTUSE ISOSCELES triangle -- where and is the obtuse vertex angle.
PAB PA PBAPB
XYZXY XZ ZXY
What observation can you make about the base angles?
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Isosceles Triangle TheoremIf two sides of a triangle are congruent,
then the angles opposite them are congruent.
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Use ALGEBRA to find the missing measures(not drawn to scale)1.
44
x y
30
mr
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Use ALGEBRA to find the missing measures(not drawn to scale)1.
44
x y
30
mr
x+y+ 44 = 180 Sumx = y because the two
base angles are congruent to each other b/c they are opposite congruent sides
180 = x + x + 44 136 = 2x68=x68 = y
68 68
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Use ALGEBRA to find the missing measures(not drawn to scale)
2.
30°
mr
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Find the missing measures(not drawn to scale)
30 + r + m = 180r is the other base
angle and must be 30° b/c its opposite from a congruent side.
30 + 30 + m = 18060 + m = 180m = 120
2.
30°
mr30°12
0°
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Isosceles Triangle TheoremIf two sides of a triangle are congruent,
then the angles opposite them are congruent.
Given: Prove:
NC NYC Y
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Proof of Base Angles TheoremGiven: Prove:
3. CH HY
4. NH NH
NC NY C Y Statements
1. Label H as the midpoint of CY
2. Draw NH
5. NC NY6. NHC NHY
7. C Y
Reasons
1. Ruler Postulate2. 2 points determine a
line
3. Def. of midpoint
4. Reflexive Prop
5. Given
6. SSS
7. CPCTC
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Converse of the Isosceles Triangle TheoremIf two angles of a triangle are congruent,
then the sides opposite them are congruent.
A
R
T
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Corollary--A corollary is a theorem that follows easily
from a theorem that has already been prove.
Corollary : If triangle is equilateral, then it is also equiangular. A
B C•Corollary : If a triangle is equiangular, then it is also equilateral. W
E R