Upload
smiller5
View
1.675
Download
1
Embed Size (px)
DESCRIPTION
Identify similar polygons Prove certain triangles are similar by using AA~, SSS~, and SAS~ Use triangle similarity to solve problems.
Citation preview
2. similar polygonsTwo polygons are similar if and only if their corresponding angles are congruent and their corresponding side lengths are proportional. Example: 6N5 3MO4 L12X810EN X L S E A O MS6A3 4 5 6 = = = 6 8 10 12 NOEL ~ XMAS 3. Note: A similarity statement describes two similar polygons by listing their corresponding vertices. Example: NOEL ~ XMAS Note: To check whether two ratios are equal, cross-multiply themthe products should be equal. Example:3 4 = 6 8 24 = 24 4. ExampleDetermine whether the rectangles are similar. If so, write the similarity ratio and a similarity statement. Q15U6 DA R25E10 TCAll of the angles are right angles, so all the angles are congruent. QUAD ~ RECT 6 15 = ? sim. ratio: 3 10 25 5 150 = 150 5. Angle-Angle Similarity (AA~) If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. P MADC OM P A O Therefore, MAC ~ POD by AA~ 6. Side-Side-Side Similarity (SSS~) If the three sides of one triangle are proportional to the three corresponding sides of another triangle, then the triangles are similar. N 18W123024H 40O 16Y TWH HY WY = = NO OT NTTherefore, WHY ~ NOT by SSS~ 7. Side-Angle-Side Similarity (SAS~) If two sides of one triangle are proportional to two sides of another triangle, and the included angles are congruent, then the triangles are similar. E U 52.5 L2VLU LV = TE TXT4XL TTherefore, LUV ~ TEX by SAS~ 8. ExampleExplain why the triangles are similar and write a similarity statement. X 34LE 56UV T90 56 = 34 Therefore mV = mX, thus V X. Since mU = mE = 90, U E Therefore, LUV ~ TEX by AA~ 9. ExampleVerify that SAT ~ ORT R 20 S12 15T 16OAATS RTO (Vertical angles ) 12 15 = ? 16 20 240 = 240 Therefore, SAT ~ ORT by SAS~