Parts of Similar Triangles

1
Parts of Similar Triangles

• Section 7.5

2
Proportional Perimeters Theorem

• If two triangles are similar, then the perimeters
  are proportional to the measures of the
  corresponding sides.

3

• Example 1
• Write the
  
  statement of
  proportionality
• to find the
  scale factor
• Scale factor
  2/3

4

• Find the perimeter of one triangle.
• Triangle ABC P
• Set up a proportion
  with the scale factor
  and the perimeter.

5

• Solve the proportion

6
Special Segments of Similar Triangles

• Similar triangles have corresponding altitudes
  proportional to the corresponding sides.

7

• Similar triangles have corresponding angle
  bisectors proportional to the corresponding
  sides.

8

• Similar triangles have corresponding medians
  proportional to the corresponding sides.

9
Examples

• 1. Triangle JLM triangle QST. KM and RT are
  altitudes of the respective triangles. Find RT
  if JL 12, QS 8, and KM 5

10

• Write the statement of proportionality, be sure
  to include the altitudes given.
• Fill in given information and solve

11

• Triangle EFD Triangle JKI. EG and JL are
  medians of their respective triangles. Find JL
  if EF 36, EG 18, and JK 56.

12
Angle Bisector Theorem

• An angle bisector in a triangle separates the
  opposite side into segments that have the same
  ratio as the other two sides