PreAlgebra 7
Summary 3.2
CMP3
Name ________________________
Period _____ Date ______________
Focus Question: What is the smallest number of side and angle measurements that will tell you how to draw an
exact copy of any given triangle?
vocabulary - congruent: same size and shape
In the Launch video, triangle congruence was introduced by exploring whether two pieces of information from
a triangle would be enough for it to be replicated. You could see that two pieces were not enough - the triangle
didn't look like the original one.
The minimum information you need about a triangle that allows you to draw exactly one like it is:
"At least three sides and/or angle measurements, but not any three."
We can draw a unique triangle given three side lengths that form a triangle; this was found in Section 3.1 using
poly strips. This is known as the Side-Side-Side Condition and is usually shortened to the SSS Condition.
From Problem 3.2, we found other conditions that produced unique triangles:
(1) Angle-Side-Angle Condition shortened to ASA Condition. Explain what is meant by these three
conditions; where is the side positioned? Sketch a triangle illustrating the ASA Condition.
(2) Side-Angle-Side Condition shortened to SAS Condition. Explain what is meant by these three
conditions; where is the angle positioned? Sketch a triangle illustrating the SAS Condition.
(3) When three angles were used, how come the resulting triangle didn't replicate the original one?
Sketch two triangles with the same corresponding angles but different sizes. (We call these triangles
similar triangles; the corresponding angles are equal but the lengths of the sides differ.)
(4) Triangle ABC has the following characteristics: angle C is 90°, side AC is 3 inches and side BC is 4
inches; draw the triangle
(5) Triangle XYZ is an isosceles triangle: angles X and Y are 45° and side XY is 2 inches long;
draw the triangle
(6) Triangle EFG is an equilateral triangle; if the sides are 1.5 inches long, draw the triangle.