4-6 Isosceles And Equilateral Triangles
You identified isosceles and equilateral triangles. Use properties of isosceles triangles.Use properties of equilateral triangles.
Isosceles TrianglesPartsleglegbaseBase anglesvertexVertex angle
The Isosceles Have It!An isosceles triangle has been drawn on a piece of paper and then cut out. (How do you draw an isosceles triangle on a piece of paper?) If the triangle is folded in half, what can be said about the base angles?What can be said about the sides?
Isosceles Triangle TheoremIf two side of a triangle are congruent, then the angles opposite those sides are congruent.Converse of the Isosceles Triangle TheoremIf two angles of a triangle are congruent, then the sides opposite those angles are congruent.
A. Name two unmarked congruent angles.Answer: BCA and A ____
B. Name two unmarked congruent segments.
A. Find mR.Triangle Sum TheoremmQ = 60, mP = mRSimplify.Subtract 60 from each side.Divide each side by 2.Answer: mR = 60
Since all three angles measure 60, the triangle is equiangular. Because an equiangular triangle is also equilateral, QP = QR = PR. Since QP = 5, PR = 5 by substitution.B. Find PR.Answer: PR = 5 cm
A.30B.45C.60D.65A. Find mT.
ALGEBRA Find the value of each variable.
mDFE= 60Definition of equilateral triangle4x 8 = 60Substitution4x= 68Add 8 to each side.x= 17Divide each side by 4.The triangle is equilateral, so all the sides are congruent, and the lengths of all of the sides are equal.DF= FEDefinition of equilateral triangle6y + 3= 8y 5Substitution3= 2y 5Subtract 6y from each side.8= 2yAdd 5 to each side. 4= yDivide each side by 2.Answer: x = 17, y = 4
Try ItWhat else must be true?3x+84x10MNOABC
What makes an isosceles unique?An isosceles triangle has two congruent sides and two congruent base angles.
What is an auxiliary line?Auxiliary line is a line (or part of a line) added to a figure.
4-6 AssignmentPage 289, 1-2, 15-22, 29-32