Similar Triangles by AA Theorem

• Not Similar
• Similar. ∆ABC~∆EDF
• Similar. ∆ACB~∆EDF
• Similar. ∆ABC~∆EFD

• Not Similar
• Similar. ∆GHI~∆JKL
• Similar. ∆GIH~∆JKL
• Similar. ∆GHI~∆JLK

• Not Similar
• Similar. ∆MNP~∆RQS
• Similar. ∆MNP~∆QRS
• Similar. ∆NPM~∆QRS

• Not Similar
• Similar. ∆MNP~∆RQS
• Similar. ∆MNP~∆QRS
• Similar. ∆NPM~∆QRS

• 25
• 16
• 9
• 7

Are these triangles similar?
Angles in Triangle 1:  40⁰,60⁰, and 80⁰
Angles in Triangle 2:  40⁰,50⁰, and 90⁰

• Yes
• No
• There is not enough information to decide.

To find the height of a very tall pine tree, you place a mirror on the ground and stand where you can see the top of the pine tree.  How tall is the tree?

• 144 feet
• 72 feet
• 36 feet

• Similar, 2 pairs of congruent angles.
  ∆JKL~∆LMN
• Similar. Side ratios proportional.
  ∆LMN~∆JKN
• Not Similar
• Similar. Perpendicular lines.
  ∆JKN~∆LMN

• Similar, 2 pairs of congruent angles.
  ∆QRP~∆TRS
• Similar, 2 pairs of congruent angles.
  ∆QRP~∆SRT
• Not Similar
• Similar, 2 pairs of congruent angles.
  ∆QRP~∆STR

The triangles are similar by...

• SAS
• AA
• ASA
• SSS