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Milestones Unit 1-2 Review
Triangle Similarity
- Similar figures in geometry have the same shape but not necessarily the same size. Because of this, we
can say that similar figures are proportional to each other.
-Similar figures have two properties:
1) Corresponding angles are congruent.
2) Corresponding sides have the same ratio. This ratio
is also called the scale factor.
Examples: For the following similar figures, identify the congruent angles and write a proportionality
statement for the lengths of the sides.
1. ABCD ∼WXYZ
2) ∆FGH ∼∆JKL
Proving Triangles are Similar
There are three methods that can be used to show whether triangles are similar or not. The three
methods are:
1) SSS
2)SAS
3) AA
Examples: Determine if the triangles are similar or not. If similar, write the theorem that would prove
them similar.
1.
2.
3.
Using Similarity
Since sides are proportional, we can use that to find missing information about similar triangles
Examples: The triangles shown are similar. Find the side of the triangle that is missing.
1.
2.
3. Find SU
Triangle Congruence
-Congruent figures are figures that have the same shape and the same size. That is to say that all of the
angles are congruent and all of the sides are congruent.
-When working with triangles, there are five theorems that will prove triangles are congruent.
1) SSS
2) SAS
3) ASA
4) AAS
5) HL
Examples: Determine if the following triangles are congruent. If congruent, state which theorem proves
congruence.
1.
2.
3.
4.
5.
6.
Examples: For the given triangles, state what additional information is needed to prove the triangles are
congruent using the stated congruence theorem.
1.
2.
3.
4.
Congruence Proofs
The congruence theorems are used to help write proofs to show the validity of a statement.
Examples: Complete the following proofs.
1. Given:
Prove:
2. Given:
Prove:
Statements:
Reasons:
Statements:
Reasons:
1)
1) Given
1)
1) Given
3. Given:
Prove:
4. Given:
Prove:
Statements:
Reasons:
Statements:
Reasons:
1)
1) Given
1)
1) Given