4.2: Similar Triangle Theorems WELCOME 4.2: Similar Triangle Theorems Last Night’s HW: 4.1 Extra Handout Tonight’s HW: 4.2 Handout

Fill in the blanks: (Write the whole sentence) Warm Up Fill in the blanks: (Write the whole sentence) I know two shapes are similar if corresponding angles are _____ and corresponding sides are ____. 2. Triangle ABC has vertices A (3,2), B(5,0) and C(4,6). What are the vertices of the image after a dilation with a scale factor of ½ using the origin as the center of dilation? 3. The polygons are similar. Find the missing side length.

Chapter 4.2 Learning Targets

Homework Review

Similar Polygons If ∠A ≌ ∠E & ∠B ≌ ∠F ∠C ≌ ∠G Then All corresponding angles are ≌ and all corresponding sides are proportional A If ∠A ≌ ∠E & ∠B ≌ ∠F ∠C ≌ ∠G Scale Factor = Then “ABC is Similar to EFG” E G F C B ABC ∼ EFG

….there is an easier way. Are the triangles similar? A S M R E B 20° 75° 27 33 11 5 M 20° 85° R 9 E 85° 75° B 15 ….there is an easier way.

What do you need to prove that ∆𝐀𝐁𝐂~∆XYZ ? B C Y Z ….there is an easier way.

Angle-Angle Similarity In Triangles (AA) If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar. A If ∠A≌∠E ∠B≌∠F Then ABC ∼ EFG E B G F C

Side-Side-Side ∆ Similarity Side-Angle-Side ∆ Similarity Triangle Similarity Side-Side-Side ∆ Similarity Side-Angle-Side ∆ Similarity If a set of angles are ≌ and the corresponding adjacent sides are proportionally equal then the ∆’s are similar. If the lengths of corresponding sides are proportionally equal then the ∆’s are similar. A E A E G F G F C B C B ∠B ≌ ∠F

Proving 2 triangles are similar: Read and understand problem. Draw all the given info on the triangle. See what else you can deduce. (Vertical angles, Linear Pair, Reflexive, Alternate Interior…) Decide Similarity Type & write at bottom of proof. (AA, SSS, SAS) 5) Start with Given and Prove Each S/A. 6) Reread proof and make sure it makes sense.

Example

Similar Triangle Sort Cut out the 16 diagrams and sort them by their similarity using the markings and given information. (AA, SAS, SSS) Then, match each diagram to the corresponding similarity statement (along the left side of the template) Once all the diagrams are arranged, call Mrs. Hower over to check