Notes for Section 4.7 - Geometry

1. Section 4.7
Use Isosceles and Equilateral
Triangles

2. 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

3. 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.

4. Example 1 Find the unknown
measure.

5. Example 2: Find the value of x.

6. Example 3: Find the values of x and y.

7. Example 4: Find the perimeter of the
triangle.

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

9. Find the measures of
R,  S, and  T.

10. 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.

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

12. 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

13. 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