Isosceles Triangles. Leg Base Angles Base Remember– the properties of an isosceles triangle….....
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Transcript of Isosceles Triangles. Leg Base Angles Base Remember– the properties of an isosceles triangle….....
Honors GeometryIsosceles Triangles
LegLeg
BaseAngles
Base
Remember– the properties of an isosceles triangle…..
Vertex Angle
Vertex Angle
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?
Isosceles Triangle TheoremIf two sides of a triangle are congruent,
then the angles opposite them are congruent.
Use ALGEBRA to find the missing measures(not drawn to scale)1.
44
x y
30
mr
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
Use ALGEBRA to find the missing measures(not drawn to scale)
2.
30°
mr
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°
Isosceles Triangle TheoremIf two sides of a triangle are congruent,
then the angles opposite them are congruent.
Given: Prove:
NC NYC Y
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
Converse of the Isosceles Triangle TheoremIf two angles of a triangle are congruent,
then the sides opposite them are congruent.
A
R
T
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