Page 73 - Math Course 3 (Book 2)

Identifying Triangles: Angles and Sides

Use the Distance Formula
MO. 9 - L1b

Measures of the Sides of a Example

Triangle
COORDINATE GEOMETRY

Find the measures of the sides of ΔRTS. Classify
Let’s Begin the triangle by sides.

S(4, 4)
Find Missing Values

Example

ALGEBRA
Find d and the measure of each side of equilateral T(8, –1)
triangle KLM if KL = d + 2, LM = 12 – d, and
KM = 4d – 13. R(–1, –3)

K Use the distance formula to find the lengths of
each side.
(x –x )² + (y –y )²
2
1
2
1
4d – 13 d + 2
RS = (–1–4)² +(–3 – 4)²
= 25 + 49

= 74
M 12 – d L

Since ΔKLM is equilateral, each side has the same
length. So KL = KM. RT = (–1– 8)² +(–3 – (–1))²

d + 2 = 4d – 13 Substitution. = 81 + 4

2 = 3d – 13 Subtract d from each side. = 85

15 = 3d Add 13 to each side.

5 = d Divide each side by 3. ST = (4– 8)² +(4 – (–1))²

Next, substitute to find the length of each side.
= 16 + 25
d + 2 4d – 13 12 – d
= 41
5 + 2 4(5) – 13 12 – 5
7 7 7

For ΔKLM, d = 5 and the measure RS = √74 ; ST = √41 ; RT = √85
Answer Answer since all 3 sides have different
of each side is 7.
lengths, ΔRST is scalene.

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