NAME __________________________________ Period _____
Gr8 – MOD 3 – Lesson 10
8.G.A.4 : Understand that a 2-dimensional figure is similar to another if the second can be obtained from the first by a
sequence of rotations, reflections, and translations, and dilations; given two similar two-dimensional figures,
describe a sequence that exhibits the similarity between them.
8.G.A.5 : Use informal arguments to establish facts about angle sum and exterior angles of triangles, about the angles
created by parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.
STUDENT OUTCOMES

Students know an informal proof of the angle-angle (AA) criterion for similar triangles.

Students present informal arguments as to whether or not triangles are similar based on AA criterion.
REVIEW
Triangle Sum Theorem- the sum of the three angles of any triangle equal __________°.
EXAMPLE 1
Do the triangles shown appear to be similar? ________
What is the measure of angle A? _______
What is the measure of angle A’? ______
Is angle A congruent to angle A’? ______
What is the measure of angle B? _______
What is the measure of angle B’? ______
Is angle B congruent to angle B’? ______
Do the triangles have 2 pairs of corresponding angles that are congruent? __________
This means the two triangles have to be similar.
The AA CRITERION for SIMILARITY
The theorem states “Two triangles with two pairs of equal angles are similar.”
In other words, if two of the three pairs of corresponding angles in the triangles are
congruent, then the triangles have to be similar. If two pairs of angles are congruent, the
third pair will also be congruent due to the triangle sum theorem. We also know that the
lengths of the corresponding sides are equal in ratio, or proportion.
**To present an informal proof [argument] as to why triangles are similar, you must have the following:
(1) Two of the three pairs of corresponding angles in the triangles must be equal in measure-congruent.
(2) State which angles are congruent and what the angle measures are.
EXAMPLE 1 continued
Present an informal argument as to why the triangles are or are not similar.
How could you determine if angle c is congruent to angle C’?
Do you need to know if these two angles are also congruent to prove the figures are similar?
EXAMPLE 2
Are the triangles shown similar? _________
Is angle A congruent to angle A’? _________
Is angle B congruent to angle B’? _________
Is angle C congruent to angle C’? _________
Do the triangles have two pairs of corresponding angles that are congruent? ________
Present an informal argument as to why the triangles are or are not similar.
EXERCISES 1-3
1) Are the triangles shown below similar? __________
Present an informal argument as to why they are or
are not similar.
2) Are the triangles shown below similar? __________
Present an informal argument as to why they are or
are not similar.
3) Are the triangles shown below similar? __________
Present an informal argument as to why they are or are not similar.
4) Are the triangles shown below similar? _________
Present an informal argument as to why they are or are
not similar.
Closing
Two triangles are said to be SIMILAR if the triangles have ______ pairs of c__________________
angles that are c__________________ or equal in m________________.
Using the proof of the _________ ______ _____________or angle-angle criterion is enough to
state that two triangles are s___________________. This proof depends on an understanding of
dilation, angles relationships of parallel lines, and congruence.
To present an informal proof (argument) as to why triangles are similar ___________ the angles
that are corresponding and the m______________of each angle.
You may have to use the Triangle Sum theorem to find the measure of an angle in order to
determine if two triangles are similar. The sum of the three a_______ of any triangles is always
equal to _________.
Lesson Summary
Two triangles are said to be similar if they have two pairs of corresponding angles that are equal in measure.