1. Grade 10 Academic (MPM2D) Unit 5: Trigonometry Congruent & Similar triangles
Mr. Choi
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2. Type of Triangles and Some Triangles Theorems
Congruent & Similar Triangles
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3. Basic Angle Theorems / Authorities
straight 90
180 90
CBD
ABD
180
180 x z w y
x y z
180
Congruent & Similar Triangles
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4. Parallel Lines Theorems Alternate Angles (PLT-Z) Corresponding Angles (PLT-F)
Congruent & Similar Triangles
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5. Parallel Lines Theorems Interior Angles (PLT-C)
Some Triangles Theorems
Exterior Angle Theorem (EAT)
Congruent & Similar Triangles
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6. 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
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7. 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
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8. How to tell the triangles are congruent?
Congruent & Similar Triangles
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9. How to tell the triangles are congruent?
Congruent & Similar Triangles
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10. 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
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11. 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
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12. How to tell the triangles are similar?
Congruent & Similar Triangles
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13. How to tell the triangles are similar?
Congruent & Similar Triangles
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14. Example 1: Determine the unknown measures a)
Congruent & Similar Triangles
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15. Example 1: Determine the unknown measures b)
Congruent & Similar Triangles
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16. Example 1: Determine the unknown measures c)
Congruent & Similar Triangles
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17. 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
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18. Example 3: Verify the similar triangles and determine the unknown measures. a)EC DC
Congruent & Similar Triangles
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19. 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
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20. Example 4: Determine the unknown measures.DB BE DE
Congruent & Similar Triangles
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21. Homework
Work sheet: Congruent and Similar Triangles Text: P. 462 #5 - 7 Check the website for updates
Congruent & Similar Triangles
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22. End of lesson Congruent & Similar Triangles
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