Section 4.7 Use Isosceles and Equilateral

Triangles

THEOREM 4.7: BASE ANGLES THEOREM

If two sides of a triangle are congruent, then the angles opposite them are congruent.

If AB AC, then B C

THEOREM 4.8: CONVERSE OF BASE ANGLES THEOREM

If two angles of a triangle are congruent, then the sides opposite them are congruent.

If B C, then AB AC.

Example 1 Find the unknown measure.

Example 2: Find the value of x.

Example 3: Find the values of x and y.

Example 4: Find the perimeter of the triangle.

Example 5: Garden You plant a garden in the shape of a triangle as shown in the figure. What is the perimeter

Find the measures ofR, S, and T.

Unit 5.1 - Notes

midsegment_ – a segment that connects the midpoint of two sides of a triangle.

So LM, MN, and LN are the midsegments of triangle ABC.

Midsegment Theorem:

The segment connecting the midpoints of two sides of a triangle is parallel to the third side and half its length.

EX 1:If QR = 18, then JK is half of it which means JK = 9.

If PK = 8, then KR = 8 since K is the midpoint of PR.

Since PR = 16 all together, JL is half of PR since it is between the two midpoints so JL = 8.

If KL = 6, then PQ is double KL so PQ = 12.

KR = 8, LR = 9, QL = 9, PJ = 6, JQ = 6

Perimeter of PQR = 18 + 12 + 16 = 46

Perimeter of JKL = 6 + 8 + 9 = 23

EX 2: Place each figure in a coordinate plane in a way that is convenient for finding side lengths.

Assign coordinates to each vertex.

a) a square with sides of length m

b) an acute triangle with base length b