Triangle Theorem Notes. Warm Up. List 5 things you think you know about triangles.
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1 Warm Up List 5 things you think you know about triangles.
2 Standards for this week: CO.10 Prove theorems about and classify triangles. Theorems include: measures of interior angles of a triangle sum to 180 degrees; base angles of isosceles triangles are congruent; Exterior Angle Theorem; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. rems about triangles. Theorems include: o one side of a triangle divides the other two
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4 O P MN=16, NO=16 a. Explain why MNO is an isosceles right triangle. M N Q b. Identify the hypotenuse and legs of MNO
5 Practice classifying: 1,3,5,7
6 Standards CO.10 Prove theorems about and classify triangles. Theorems include: measures of interior angles of a triangle sum to 180 degrees; base angles of isosceles triangles are congruent; Exterior Angle Theorem; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. SRT.4 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally
7 Triangle Sum Theorem Do you remember the triangle sum theorem? What did it say?
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10 Priority Standards
11 Make 4 groups of angles that form a triangle o 30 o 90 o 60 o 45 o 90 o 64 o 45 o 62 o 54 o Classify the triangles you made.
12 Standards CO.10 Prove theorems about and classify triangles. Theorems include: measures of interior angles of a triangle sum to 180 degrees; base angles of isosceles triangles are congruent; Exterior Angle Theorem; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. SRT.4 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally
13 Prove the Base Angles Theorem: If two sides of a triangle are congruent, then the angles opposite those sides are congruent. B A E S Given: Prove: E is the midpoint of BS
14 Find an Isosceles triangle whose base angles are 26 o. T 128 o Find an Isosceles triangle whose base angles are 43 o. S 94 o R I C E Find an Isosceles triangle whose base angles are 64 L o. 52 o Find an Isosceles triangle whose base angles are 77 o. I 26 o E S S O
15 Standards CO.10 Prove theorems about and classify triangles. Theorems include: measures of interior angles of a triangle sum to 180 degrees; base angles of isosceles triangles are congruent; Exterior Angle Theorem; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. SRT.4 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally
16 Exterior Angle the angle between any side of a shape, and a line extended from the next side.
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19 5 Practice Problems 5, 7, 13,
20 Standards CO.10 Prove theorems about and classify triangles. Theorems include: measures of interior angles of a triangle sum to 180 degrees; base angles of isosceles triangles are congruent; Exterior Angle Theorem the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. SRT.4 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally
21 Review: Put in notes Classify the following triangles by side and angle Triangle Theorems Complete each statement using always, sometimes or never. An Isosceles triangle is an equilateral triangle An Obtuse triangle is an isosceles triangle. An interior angle of a triangle and one of it's adjacent exterior angles are supplementary The acute angles of a right triangle are complementary. A triangle has a right angle and obtuse angle
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24 A couple more examples 4)
25 Try some on your own:
26 Standards CO.10 Prove theorems about and classify triangles. Theorems include: measures of interior angles of a triangle sum to 180 degrees; base angles of isosceles triangles are congruent; Exterior Angle Theorem the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. SRT.4 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally
27 Review 1. Classify the following triangle by angles and sides. 2. Determine the value of x. 4x+25 2x x Determine the length of AE. mag = 10x mge = 2x+9
28 Warm Up The variable expressions represent angle measures of a triangle. Draw a triangle and label the angles. Solve for x and determine value of each angle. 1. m A = x m =2x m C =3x B 2. m D= (3x 17) m E= (x+40) m F =(2x 5)
29 Standards CO.10 Prove theorems about and classify triangles. Theorems include: measures of interior angles of a triangle sum to 180 degrees; base angles of isosceles triangles are congruent; Exterior Angle Theorem the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. SRT.4 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally
30 FOLDABLE Triangle Theorems Triangle Proportionality Theorem: Triangle Midsegment Theorem: Midsegment Parallel Line
31 On the inside Triangle Proportionality Theorem: A line parallel to one side of a triangle divides the other two proportionally, and its converse. Ex. 1 Ex x 8 x 10 6 Ex. 1 Ex. 2 x 18 Midsegment of a Triangle : 1. Parallel to one side 2. Midsegment is 1/2 the length of the parallel side 3. Midsegment contacts the midpoints. Equation: midsegment = 1/2 parallel side 12 y
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33 Similarity and Triangles Recap: 1. Two ladders are leaned against a wall such that they are parallel with each other. The shorter ladder's feet are 12' from the wall and reaches 8' up the wall. The taller ladder's feet are 15' from the wall, how much further up the wall does the taller ladder reach? 2. Find the value of x. 3x 5 11
34 Standards CO.10 Prove theorems about and classify triangles. Theorems include: measures of interior angles of a triangle sum to 180 degrees; base angles of isosceles triangles are congruent; Exterior Angle Theorem the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. SRT.4 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally
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