Lessons

1. Basics
 2. Deductive Reasoning
3 - Parallel lines
4 - Congruent Triangles
5 - Quadrilaterals
6 - Inequalities
7 - Similar Polygon
8 - Rt. Triangles
9 - Circles
10 - Constructions
11 - Areas of 2D objects
12 - Areas and Volumes
13 - Coordinates

 

Similar Triangles

 

Objective:

            • Learning about the AA Similarity Postulate, the SAS Similarity Theorem, and the SSS Similartiy Theorem

           • Apply the Triangle Proportionality Theorem and its corollary and the Triangle Angle- Bisector Theorem

 

Lesson 7-3 Similar Triangles

            

Postulate 15 (AA Similarity Postulate)

If two angles of one triangle are congruent to two angles of another triangle, then the triangle are similar

Triangle ABC is similar to triangle DEF

 

Theorem 7-1 (SAS Similarity Theorem)

If an angle of one triangle is congruent to an angle of another triangle and the sides including those angles are in proportions, then the triangles are similar

Triangle ABC is similar to triangle DEF because / A and / D are congruent and AB/DE = AC/DF

 

Theorem 7-2 (SSS Similarity Theorem)

If the sides of two triangles are in proportion, then the triangles are similar

AB/DE = AC/DF = BC/EF

The two triangles are similar

 

Theorem 7-3 (Triangle Proportionality Theorem)

If a line parallel to one side of a triangle intersects the other two sides, then it divides those sides proportionally.

Segment DG/GE = Segment FH/HE

 

Corollary

If three parallel lines intersect two transversals, then they divide the transversals proportionally.

Segment AB/BC = Segment DE/EF

 

Theorem 7-4 (Triangle Angle-Bisector Theorem)

If a ray bisects an angle of a triangle, then it divides the opposite side into segments proportional to the other two sides.

Segment AB/BC = Segment DA/DC

 

 

 

 

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