Transcript 11/4 Isosceles, Equilateral, and Right Triangles File

Unit 1B2 Day 12
Do Now

Fill in the chart:
Acute
Triangle
# of Acute
Angles
# of Right
Angles
# of Obtuse
Angles
Right
Triangle
Obtuse
Triangle
Isosceles Triangles: Vocab.

 The two congruent sides are called
the ________.
 The remaining side is called the
_________.
 The two angles opposite the legs
are called the __________ angles.
 The remaining angles is called the
___________ angle.
Investigating Base Angles

Use a straightedge to construct an acute
isosceles (columns 1 and 3) or an obtuse
isosceles (columns 2 and 4) triangle.
Fold the triangle along a line that bisects the
vertex angle.
What do you observe about the base angles?
Compare with someone next to you.
Base Angles Theorem (Thm.
4.6)

If two sides of a triangle
are congruent, then the
angles opposite them are
_______________.
 If AB ≅ AC, then
_________.
B
A
C
Base Angles Converse (Thm. 4.7)
If two angles of a
triangle are
congruent, then
__________________
__________________

B
A
 If B ≅ C, then
_______________
C
Ex. 1: Proof of the Base Angles
Thm.
Given: AB ≅ AC
Prove: B ≅ C

B
A
C
Corollaries

Corollary to theorem 4.6—If a triangle is
equilateral, then __________________.
Corollary to theorem 4.7– If a triangle is
equiangular, then _________________.
A
B
C
Ex. 2: Using Equilateral and Isosceles
Triangles

 Find the values of x and y.
Ex. 2a

Find the values of x and y.
Do now

Find the value of x.
Right Triangles

For two right triangles, if both pairs of legs are
congruent, then you can prove the triangles are
congruent using ______.
BUT there’s
another way to
prove right
triangles are
congruent…
Hypotenuse-Leg (HL)
Congruence Theorem

If the hypotenuse and a leg of a right triangle
are congruent to the hypotenuse and a leg of a
second right triangle, then ________________
 If BC ≅ EF and AC ≅ DF, then ∆ABC ≅ ∆DEF.
 MUST be right triangles!
Ex. 3: Proving Right
Triangles Congruent

Given: AD  CB, AC ≅ AB
Prove: ∆ACD ≅ ∆ABD
Ex. 4: Proving Right
Triangles Congruent

Given: AE  EB, AE  EC, AE 
 The television antenna
is perpendicular to the ED, AB ≅ AC ≅ AD.
Prove: ∆AEB ≅ ∆AEC ≅ ∆AED
ground.
 Each of the lines
running from the top of
the antenna to B, C, and
D uses the same length
of cable.
More Examples

 Is there enough
information to
prove that the
triangles are
congruent?
Explain!
6.
5.
7.
Closure

Can you use HL to prove that two
isosceles triangles are congruent?