Topic: Lesson 8-3 (Proving Triangles Similar)

Class: Honors Geometry Date: Topic: Lesson 8-3 (Proving Triangles Similar) Postulate 8-1 AA~ Angle-Angle Similarity (AA~) T P If 2 's of D are @ to 2 's of another D , then the D 's are ~. S 蠤行 R If T P& R@ L then M DTRS~ D PLM L

Side-Angle-Side Similarity (SAS~) Theorem 8-1 SAS~ A If an of 1 D is @ to an of another D , Q and the sides incl the @ 's are proportional, then the D 's are ~. B C AB AC R S If蠤A� Q & then QR QS DABC~ D QRS Theorem 8-2 SSS~ Side-Side-Side Similarity (SSS~) A Q If the corr sides of 2 D 's are proportional, then the D 's are ~. B C S AB AC BC R If = = then QR QS RS DABC~ D QRS Triangle Similarity Examples 1. MX^ AB . Explain why D 's are ~. Write a similarity stmt. Have info & no length info so look at AA~ & SAS~. 行AXM& BXK are right 's and therefore are @ . m� A � m蠤 B58, so A B We have two @ 's so we’re done. Therefore DAXM~ D BXK by AA~ Postulate.

2. Explain why D 's are ~. Write a similarity stmt. W Z 24 Look for either AA~, SAS~ 18 or SSS~. V

蠤ZVY WVX (vert 's ) 12 Y 36 Hmm, only set we have @ X … VY12 1 VZ 18 1 VY VZ = =& = = so = VW24 2 VX 36 2 VW VX Page 1 of 3 Class: Honors Geometry Date: Topic: Lesson 8-3 (Proving Triangles Similar)

So DZVY~ D XVW by SAS~ Theorem

3. ABCD is a parallelogram. Find WY. Have lots of side len info so let’s look for SAS~ or SSS~. Don’t have the lens of all 3 sides so work on SAS~. We first need to determine corresponding sides.

It’s a parallelogram, so ABP DC with AY& XZ transv. 蠤AXW 行 YZW& WAX@ WYZ (alt. int. s ).

So DAXW~ D YZW by AA~ A X B Postulate. 5 4

Thus, XW corr w/ ZW & AW W w/YW . 20 AW XW D We then have = Z Y C WY ZW and Indirect AW5 XW 4 1 =& = = Measurement WY WY ZW 20 5 5 1 So =;WY = 5g 5 = 25 Example WY 5

Using ~D 's to find measurements difficult to obtain directly. Light reflects off surf at same it hits the surf

4. Joan places a mirror 24 ft fm the base of a tree. When she stands 3 ft fm the mirror, she can see h the top of the tree 5 ft reflected in it. If her eyes are 5 ft above the 3 ft 24 ft ground, how tall is the tree?

1st look for AA~, SAS~ or SSS~. Have 2 rt D 's . Also the s formed at the mirror are @ (light reflection). Thus we Page 2 of 3 Class: Honors Geometry Date: Topic: Lesson 8-3 (Proving Triangles Similar) have 2 @ 's so the 2 D 's are ~ by the AA~ Postulate. The distance to the mirror legs correspond; the height legs correspond. Thus we have the following proportional statement: 5h 120 =; 3h = 5g 24; h = = 40 ft 3 24 3