Grade 10 Academic (MPM2D) Unit 5: Trigonometry Congruent & Similar triangles Mr. Choi © 2017 E. Choi – MPM2D - All Rights Reserved
Type of Triangles and Some Triangles Theorems Congruent & Similar Triangles © 2017 E. Choi – MPM2D - All Rights Reserved
Basic Angle Theorems / Authorities straight 90 180 90 CBD ABD 180 180 x z w y x y z 180 Congruent & Similar Triangles © 2017 E. Choi – MPM2D - All Rights Reserved
Parallel Lines Theorems Alternate Angles (PLT-Z) Corresponding Angles (PLT-F) Congruent & Similar Triangles © 2017 E. Choi – MPM2D - All Rights Reserved
Parallel Lines Theorems Interior Angles (PLT-C) Some Triangles Theorems Exterior Angle Theorem (EAT) Congruent & Similar Triangles © 2017 E. Choi – MPM2D - All Rights Reserved
Congruent Triangles When two triangles are congruent they will have exactly the same three sides and exactly the same three angles. The equal sides and angles may not be in the same position (if there is a turn or a flip), but they are there. Congruent & Similar Triangles © 2017 E. Choi – MPM2D - All Rights Reserved
How to tell the triangles are congruent? Any triangle is defined by six measures (three sides, three angles). But you don't need to know all of them to show that two triangles are congruent. Various groups of three will do. Triangles are congruent if: Congruent & Similar Triangles © 2017 E. Choi – MPM2D - All Rights Reserved
How to tell the triangles are congruent? Congruent & Similar Triangles © 2017 E. Choi – MPM2D - All Rights Reserved
How to tell the triangles are congruent? Congruent & Similar Triangles © 2017 E. Choi – MPM2D - All Rights Reserved
Similar Triangles Two triangles are similar if the only difference is size (and possibly the need to turn or flip one around). Equal angles have been marked with the same label or same number of arcs) Some of them have different sizes and some of them have been turned or flipped. Similar triangles have all their angles equal and their corresponding sides have the same ratio. Congruent & Similar Triangles © 2017 E. Choi – MPM2D - All Rights Reserved
How to tell the triangles are similar? Any triangle is defined by six measures (three sides, three angles). But you don't need to know all of them to show that two triangles are similar. Various groups of three will do. Triangles are similar if: Congruent & Similar Triangles © 2017 E. Choi – MPM2D - All Rights Reserved
How to tell the triangles are similar? Congruent & Similar Triangles © 2017 E. Choi – MPM2D - All Rights Reserved
How to tell the triangles are similar? Congruent & Similar Triangles © 2017 E. Choi – MPM2D - All Rights Reserved
Example 1: Determine the unknown measures a) Congruent & Similar Triangles © 2017 E. Choi – MPM2D - All Rights Reserved
Example 1: Determine the unknown measures b) Congruent & Similar Triangles © 2017 E. Choi – MPM2D - All Rights Reserved
Example 1: Determine the unknown measures c) Congruent & Similar Triangles © 2017 E. Choi – MPM2D - All Rights Reserved
Example 2: Verify the congruent triangles and determine the unknown measures. B C D E 3 cm 1 cm 4 cm 5 cm x Congruent & Similar Triangles © 2017 E. Choi – MPM2D - All Rights Reserved
Example 3: Verify the similar triangles and determine the unknown measures. a) EC DC Congruent & Similar Triangles © 2017 E. Choi – MPM2D - All Rights Reserved
Example 3: Verify the similar triangles and determine the unknown measures. b) M N P Q LP LQ PQ Since triangle is not labelled, it is easier to label it in your own way like above before you continue. LMNPQ Congruent & Similar Triangles © 2017 E. Choi – MPM2D - All Rights Reserved
Example 4: Determine the unknown measures. DB BE DE Congruent & Similar Triangles © 2017 E. Choi – MPM2D - All Rights Reserved
Homework Work sheet: Congruent and Similar Triangles Text: P. 462 #5 - 7 Check the website for updates Congruent & Similar Triangles © 2017 E. Choi – MPM2D - All Rights Reserved
End of lesson Congruent & Similar Triangles © 2017 E. Choi – MPM2D - All Rights Reserved