Name _______________________________________
Date __________________
Hour ___________
Problem 2.3 Congruent Triangles II
Focus Question: What is the smallest number of side and/or angle measurements needed to conclude that
two triangles are congruent??
A. Can you be sure that two triangles are congruent if you have information about one pair of
corresponding sides or corresponding angles? Let’s see.
1. Draw a triangle with one side that measures 5cm long. Compare your triangle with other
students in your group. Are the triangles congruent?
2. Draw a triangle with one angle that measures 50°. Compare your triangle with other
students in your group. Are the triangles congruent?
Butterflies, Pinwheels, and Wallpaper
Investigation 2: Transformations and Congruence
B. Can you be sure that two triangles are congruent if you have information about two pairs of
corresponding sides or corresponding angles? Let’s see.
1. The triangle below has sides of 4cm and 6cm. Can you draw another triangle with sides
measuring 4cm and 6cm long that is NOT congruent to the triangle below?
4cm
6cm
2. The triangle below has angles of 90° and 20°. Can you draw another triangle with angles that
measure 90° and 20° that is NOT congruent to the triangle below?
20°
3. The triangle below has an angle measuring 60° and a side that is 5cm long. Can you draw
another triangle with an angle that measures 60° and a side of 5cm that is NOT congruent
to the triangle below?
60°
5cm
Butterflies, Pinwheels, and Wallpaper
Investigation 2: Transformations and Congruence
C. Can you be sure that two triangles are congruent if you have information about three pairs of
corresponding sides or corresponding angles? Let’s see.
1. The triangles below have two pair of congruent corresponding angles and one pair of
congruent corresponding sides as shown. Are they congruent? ___________________
If yes, what transformations can you use to show that the triangles are congruent?
2. The triangles below have two pair of congruent corresponding sides and one pair of
congruent corresponding angles as shown. Are they congruent? ___________________
If yes, what transformations can you use to show that the triangles are congruent?
D. Can you be sure that two triangles are congruent if you have information about any three pairs
of corresponding sides or corresponding angles? Let’s see.
1. The triangles below have three pairs of congruent corresponding angles as shown. Are they
congruent? ____________ If yes, what transformations can you use to show that the triangles
are congruent?
Butterflies, Pinwheels, and Wallpaper
Investigation 2: Transformations and Congruence
2. What combinations of three congruent corresponding parts will guarantee two triangles are
congruent?
There are 4 ways to prove that two triangles are congruent without knowing the measures of all the
angles and all the sides.
Methods for Proving Triangles are Congruent
SSS
If three sides of one triangle are congruent to three sides of
another triangle, the triangles are congruent.
SAS
If two sides and the included angle of one triangle are
congruent to the corresponding parts of another triangle, the
triangles are congruent. (The included angle is the angle
formed by the sides being used.)
ASA
If two angles and the included side of one triangle are
congruent to the corresponding parts of another triangle, the
triangles are congruent. (The included side is the side
between the angles being used. It is the side where the rays of
the angles would overlap.)
AAS
If two angles and the non-included side of one triangle are
congruent to the corresponding parts of another triangle, the
triangles are congruent. (The non-included side can be either
of the two sides that are not between the two angles being
used.)
The information below is NOT enough to prove that triangles are congruent.
AAA
Butterflies, Pinwheels, and Wallpaper
SSA
Investigation 2: Transformations and Congruence