Download Similar Triangles

Similar Triangles
Table of Contents
Similar Triangles ............................................................................................................................................ 2
Problem 1: Use Similar Triangles - Using Shadow to find Height of Store (Easy) .................................... 5
Problem 2: Use Similar Triangles -Using Mirror to find Height (Medium)............................................... 5
Problem 3: Use Similar Triangles - Using Shadow to find Height of Building (Easy)................................. 6
Answers ......................................................................................................................................................... 7
Geometry
1
Similar Triangles
Similar Triangles
Similar Triangles have the save shape.
Similar Triangles have the same shape, but
can be different sizes.Corresponding angles
are the same and
Corresponding sides are all in the same
proportion
How to prove if triangles are similar
A triangle is defined by six measures (three sides, three
angles). Triangles are similar if:
AAA (angle angle angle)
All three pairs of corresponding angles are the same.
SSS in same proportion (side side side)
All three pairs of corresponding sides are in the same
proportion
SAS (side angle side)
Two pairs of sides in the same proportion and the included
angle equal.
Geometry
2
Parallel Theorem:
Similar Triangles
1. If two parallel lines are transected by a third, the alternate interior angles are the
same size.
2: If two parallel lines are transected by a third, the alternate exterior angles are the
same size.
3: If two parallel lines
are cut by a transversal, the interior angles on the same side of
the transversal are supplementary.
Definitions:
Transversal is a line that intersects two or more lines (in the same plane).
Geometry
3
Similar Triangles
Problem:
Jack stands 6 feet tall and cast a shadow of 5 feet. The light pole cast a shadow of
30 feet. How tall is the light pole?
6 ft
x
5 ft
30 feet
30 ft
The two triangles are similar because their angles are equal.
Therefore, their sides are proportional.
6/x = 5/30
6 = (1/6)x
36 = x
Geometry
4
Similar Triangles
Problem 1: Use Similar Triangles - Using Shadow to find
Height of Store (Easy)
Jackie stands 5 feet tall and cast a shadow of 4 feet. The grocery store cast a
shadow of 40 feet.
a. How tall is the store?
Problem 2: Use Similar Triangles -Using Mirror to find
Height (Medium)
Buddy is 2 m tall. He is standing in front of a tree. His friend Carol places a mirror
on the ground and moves it until Bill can see the top of the tree. The mirror is 3m
from Bill and 16m from the tree.
a.
How tall is the tree?
Geometry
5
Similar Triangles
Problem 3: Use Similar Triangles - Using Shadow to find
Height of Building (Easy)
Will stands 7 feet tall and cast a shadow of 6 feet. The school building cast a
shadow of 44 feet.
a. How tall is the school?
Geometry
6
Answers
Similar Triangles
1a: 48 feet
2a: 10.67 m
3a: 51.33 feet
Geometry
7