Download Section 4.3: Isosceles and Equilateral Triangles

3 acute angles
1 right angle, 2 acute angles
1 obtuse angle, 2 acute angles
3 congruent acute angles
Goal: Use properties of Isosceles and Equilateral triangles to
find angle and side measures.
 Legs (of an isosceles ∆): The
congruent sides of an Isosceles
triangle.
 Base (of an isosceles ∆): The
other/non-congruent side of
an Isosceles triangle.
 Base angles: The two angles at the base of an Isosceles
triangle. (the two congruent angles.)
 Find the measure of ∠𝐿.
 Angle L is a base angle
of an isosceles triangle.
The measure of ∠𝐿 = 52°.
 Find the value of x.
 The base angles are the same
so the legs should also be the
same length.
𝐷𝐸 = 𝐷𝐹
𝑥 + 3 = 12
𝑥=9
 What is the value of x?
𝐦∠𝑪 + 𝒎∠𝑩𝑫𝑪 + 𝒎∠𝑫𝑩𝑪 = 𝟏𝟖𝟎
𝟓𝟒 + 𝟗𝟎 + 𝒙 = 𝟏𝟖𝟎
𝒙 = 𝟑𝟔°
 Find the length of each side of
the equiangular triangle.
 Since ∆𝑄𝑅𝑇 is equiangular it is
also equilateral.
3𝑥 = 2𝑥 + 10
𝑥 = 10
3 10 = 30
Each side of ∆𝑄𝑅𝑇 is 30.
Sub in 10 for x to find the side length.
Equilateral means sides of equal length, equiangular means
angles of equal measure.
All sides and all
angles are congruent.
∠𝑅 ≅ ∠𝑇;
∠𝑉 ≅ ∠𝑊;
𝑅𝑆 ≅ 𝑇𝑆
𝑊𝑈 ≅ 𝑉𝑈
𝑥 = 50, 𝑏𝑎𝑠𝑒 𝑎𝑛𝑔𝑙𝑒𝑠 𝑡ℎ𝑒𝑜𝑟𝑒𝑚
𝑥 = 8.8 , converse of base
angles theorem.
 p 254 – 256, #’s 6 – 32 even