Topic: Unit 4Proportions and Similarity Packet #1
G-SRT.2 Given two figures, use the definition of similarity in
terms of similarity transformations to decide if they are similar;
explain using similarity transformations the meaning of similarity
for triangles as the equality of all corresponding pairs of angles
and the proportionality of all corresponding pairs of sides.
G-SRT.5 Use congruence and similarity criteria for triangles to
solve problems and to prove relationships in geometric figures.
1. Students will be able to write ratios.
2. Students will be able to set up and solve proportions.
Solve word problems containing several rates, proportions, or
Use scale factors to determine the magnitude of a size
Draw conclusions based on a set of conditions.
Solve multistep geometry problems that involve integrating
concepts, planning, visualization, and/or making connections with
other content areas.
Use several angle properties to find an unknown angle
1. Students will be able to identify similar figures.
1. Students will be able to solve problems using scale
1. Students will be able to solve word problems applying
properties of proportions.
2. Students will be able to apply proportional parts and scale
factors to solve geometric problems.
Directions: Find the specific ratio given a scenario.
1. A designated hitter made 10 hits in 15 games. Find the ratio
of hits to games.
2. There are 80 boys in the sophomore class of 200 students.
Find the ratio of boys to girls.
Directions: Solve the following proportions.
1. = x =
2. = y =
3. = x =
4. = x =
5. = 8 a =
Question: What is the difference between a ratio and a
#1, 3-8, 28-35
The order of the vertices in a similarity statement is
important. It identifies the corresponding angles and the
Directions: Determine whether the each pair of figures is
similar. Justify your answer.
#4, 5, 6, 7, 11-14
Directions: The polygons in each pair are similar. Find the
scale factor of the smallest figure to the larger figure.
#1, 15, 21-23, 53-55
1. In a triangle, the ratio of the measures of three sides is
5:12:13, and the perimeter is 90 centimeters. Find the measure of
the shortest side of the triangle.
2. The ratio of the measures of the three angles is 2:5:3. Find
the measures of the angles of each triangle.
3. A twinjet airplane has a length of 78 meters and a wingspan
of 90 meters. A toy model is made in proportion to the real
airplane. If the wingspan of the toy is 36 centimeters, find the
length of the toy.
4. Triangle ABC is similar to triangle XYZ with a scale factor
of 2:3. If the lengths of the sides of triangle ABC are 6, 8, and
10 inches, what are the lengths of the sides of triangle XYZ?
5. The two polygons are similar. Write a similarity statement,
find x, y and UT. Find the scale factor of polygon RSTUV and
#9, 10, 19-22, 26-27
#6, 7, 34-39