Download Common Core Geometry - Honors Proving Triangles Similar – Day 1

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Common Core Geometry - Honors
Date: _________________
Proving Triangles Similar – Day 1
Ratio: a comparison of two numbers by the means of division
Proportion: Two ratios that are equal
Example:
a c

b d
**In a proportion the product of the means equals the product of the extremes.
In other words, the cross products are equal**
Example: If we look at the ratios a: b = c : d
_____ and _____ are the means, ______ and______ are the extremes.
a  d  c  b (This represents the product of the means equals
product of the extremes)
Two Triangles are similar if:


The corresponding angles are congruent
The corresponding sides are in proportion
Method to Prove Two Triangles Similar:
AA Method:

Show that two angles in one triangle are congruent to the two
corresponding angles of another triangle.
the
Checklist Procedure for proving Triangles Similar:
1. Prove two triangles similar using AA
2. Show Pairs of sides of both triangles are in a proportion by using CSSTP
(Corresponding Sides of Similar Triangles are in a Proportion)
3. Show the cross products are equal because in a proportion the product
of the means equals the products of the extremes.
Let’s try this proof…..
Given: AB ED
Prove: 1. ABC CDE
CE BC
2.

ED AB
3. CE  AB=BC  ED
Similarity Proofs
Remember: 1.) Triangles are similar by the Angle-Angle Theorem.
2.) Segments of triangles are in a proportion by CSSTP.
3.) The product of the means equals the product of the extremes.
1.
Given: Parallelogram ABCD
Prove: KM  LB=LM  KD
2.
Given : Parallelogram ABCD
Prove: AF  EF = BF  DF