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Notes Similar Figures Predict - Draw a line matching up the pairs of shapes that have the most in common… Vocabulary *Similar shapes are different _________ but have equal ___________. *Congruent means ______________. *Corresponds means __________________. Notation: *If two shapes are similar ______, their sides are proportional and their angles are congruent _______. **Congruent angles are marked with the same number of arcs. *Corresponding sides of similar figures can be found by using the names of the figures! A X C B Y Z ∆ABC ~ ∆XYZ ∠A ≅ _______ ̅̅̅̅ corresponds with _______ AB ∠B ≅ _______ ̅̅̅̅ BC corresponds with _______ ∠C ≅ _______ ̅̅̅̅ AC corresponds with _______ Symbols: ∆ ∠ ¯¯̅ ≅ ~ triangle angle side congruent similar Using Proportions with Similar Figures To determine if two figures are similar: 1. Create a proportion (draw four boxes!) 2. Label the names of the figures *Use your colors to help!* 3. Complete the proportion using corresponding sides 4. Cross multiply; if it is a true proportion, the figures are similar! Guided Practice: Z Determine whether figures ABC and XYZ are similar. *Remember to line up the names of the figures! A 15 m 6m 20 m B C X Y 8m Independent Practice: 1) Is figure LMNO similar to QRST? L 4 in M Q 12 in H S S 3 km C A 5 km D U 4 cm Y G X A X 1 km 2 km 6 cm 4) Is figure XYZ similar to ABC? 5 in T R 5 cm 3 cm 3) Is figure ABCD similar to RSTU? B W F 3 in R 9 in T N O 2) Is figure FGH similar to WXY? Z 2 in Y 9 in B 22.5 in C To find the length of a missing side using similar figures: 1. Create a proportion (draw a box!) 2. Label the names of the figures 3. Complete the proportion using corresponding sides 4. Cross multiply and divide Guided Practice: Z If ABC ~ XYZ, find the length of the missing side. A *HINT, HINT, HINT…Line up the names of the triangles to help you find corresponding sides! 10 4 15 B C X Y ? Independent Practice: Find the length of the missing sides of the figures below. 1) Figure ABCD ~ Figure WXYZ D C W 2 cm 2) Figure LMN ~ Figure RST L X 10 cm ? 16 cm A 8 cm B Z Y 20 in B D C L 2 in R 2.5 cm X S K F 10 in 8 in x in N 28 cm 4) Figure XYZ ~ Figure DEF J M x cm M 3) Figure ABCD ~ Figure JKLM A T Z 9 in x in Y E 6 in D