Similar Triangles and Parallel Lines

1/14 Geometry

Shortcuts for Similar Triangles

By Nichole Nuckols

For Congruence, we had 5 shortcuts:

For Similarity, we have 3 shortcuts:

​AA (Angle-Angle) Similarity

​If two angles in one triangle are congruent to two angles in another triangle, then the triangles are similar.

Things to Remember!!

Vertical Angles

1) ​Congruent

2) Formed by any pair of intersecting lines​

3) Share only one point, the vertex​

Things to Remember!!

The sum of all the interior angles of a triangle will always be 180.​

Triangle Angle Sum Theorem

Things to Remember!!

1) Two or more parallel lines intersected by the same transversal create special angle pairs

2) Usually use corresponding and alternating interior angles​

Transversals and Parallel Lines

​If QD is the transversal, then angles Q and D are alternating interior angles.

​If BD is the transversal, then angles BLM and BDC are corresponding angles.

Now we're going to practice using the AA shortcut.

Multiple Choice

Are the triangles similar by the AA shortcut? If yes, write the similarity statement.

• Similar; $$\triangle LMN\ \sim\triangle RPQ$$  

• Similar;   $$\triangle LMN\sim\triangle PQR$$  

• Similar; $$\triangle LMN\sim\triangle QRP$$  

• Not Similar

Multiple Choice

Are the triangles similar by the AA shortcut? If yes, write the similarity statement.

• Not Similar

• Similar; $$\triangle CDE\sim\triangle VCW$$  

• Similar; $$\triangle CDE\sim\triangle CVW$$  

• Similar; $$\triangle CDE\sim\triangle VWC$$  

Multiple Choice

Are the triangles similar by the AA shortcut? If yes, write the similarity statement.

• Not Similar

• Similar; $$\triangle QRS\sim\triangle KLQ$$  

• Similar; $$\triangle QRS\sim\triangle QKL$$  

• Similar; $$\triangle QRS\sim\triangle QLK$$

Multiple Choice

Are the triangles similar by the AA shortcut? If yes, write the similarity statement.

• Not Similar

• Similar; $$\triangle DEF\sim\triangle CBA$$

• Similar; $$\triangle DEF\sim\triangle ACB$$

• Similar; $$\triangle DEF\sim\triangle CAB$$

Multiple Choice

Are the triangles similar by the AA shortcut? If yes, write the similarity statement.

• Similar; $$\triangle BCD\sim\triangle BUV$$  

• Not Similar

• Similar; $$\triangle BCD\sim\triangle BVU$$  

• Similar; $$\triangle BCD\sim\triangle VUB$$  

​Thank you for your time and participation!

​

Please check Google Classroom and complete the linked IXL. Thank you!​

​