4.6 isosceles and equilateral triangles ink.notebook
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4.6 Isosceles and Equilateral Triangles
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Lesson Objectives Standards Lesson Notes
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4.6 Isosceles and Equilateral Triangles
4.6 isosceles and equilateral triangles ink.notebook
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November 06, 2017
Lesson Objectives
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Lesson NotesStandards
After this lesson, you should be able to successfully use theorem about isosceles and equilateral triangles to find missing parts of triangles.
Lesson Objectives Standards Lesson Notes
G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.G.CO.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.G.CO.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.
G.CO.10 Prove theorems about triangles.
Parts of a TriangleThe ⁄ formed by the legs is called the ____________________. The other two ⁄’s in an isosceles Ë are called __________________.
The 3rd side of the triangle is called the
_______________.
Isosceles triangles have two congruent sides called the __________.
Isosceles
If two sides of a triangle are congruent, then the angles opposite them are congruent.
ISOSCELES TRIANGLE THM
If AB ≅ AC, then ⁄B ≅ _______CONVERSE of ISOSCELES TRIANGLE THM
If two angles of a triangle are congruent, then the sides opposite them are congruent.If ⁄B ≅ ⁄C, then AB ≅ ______
4.6 isosceles and equilateral triangles ink.notebook
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EquilateralEQUILATERAL Ë COROLLARIES
A triangle is equilateral if and only if it is __________________.
Each angle of an equilateral triangle measures ______°.
F
G
H
In ∆FGH, FH ≅ GH.Name two congruent angles.
a)
b) 3m
R
S
T
3m
3m
Find the measures of ∠R, ∠S, and ∠T.
4.6 isosceles and equilateral triangles ink.notebook
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c)
d)
F
G
H
K J
F
G
H
K J
If ∆FGK is equiangular and FG = 15, then
GK = ______.
∠______ ≅ ∠______.
If FH ≅ FJ, then
e) f) Find xFind x
4.6 isosceles and equilateral triangles ink.notebook
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Find the value of the variable.
1. 2. Find x and m∠T. Find x, given BC ≅ BA.
Find the value of the variable.3. Find x and y. 4.
4.6 isosceles and equilateral triangles ink.notebook
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Find the value of the variable.
5. 6.
EXTRA
4.6 isosceles and equilateral triangles ink.notebook
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November 06, 2017
Prove that if a line is parallel to one side of an equilateral triangle, then it forms another equilateral triangle.
A.
On the Worksheet
PRACTICE
Find the value of the variable by writing an equation and showing all work.
1. 2.
4.6 isosceles and equilateral triangles ink.notebook
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3. 4.2x°
A
B
C(6x + 6)°
6.5.
7. 8. 9.
4.6 isosceles and equilateral triangles ink.notebook
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Refer to the figure at the right.
10.
11.
12. If ∠EBA § ∠EAB , name two congruent segments.
13. If ∠CED § ∠CDE, name two congruent segments.
Find each measure.
14. m∠ABC 15. m∠EDF
Find each measure.
16. m∠KML
17. m∠HMG
18. m∠GHM
19. If m∠HJM = 145, find m∠MHJ
20. If m∠G = 67, find m∠GHM
m∠KMH = 50 21. SPORTS A pennant for the sports teams at Lincoln High School is in the shape of an isosceles triangle. If the measure of the vertex angle is 18, find the measure of each base angle.
4.6 isosceles and equilateral triangles ink.notebook
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November 06, 2017
From the book:Find each measure.
22. m∠BAC 23. m∠SRTFrom the book:
Find each measure.
25. CB24. TR
Answers:
1. 4x + 40 = 180, x = 35 3. 14x + 12 = 180, x = 12
5. 4x – 4 = 3x + 8, x = 12 7. 2(2x + 3) + 90 = 180, x = 21
9. 6x + 12 + 90 = 180, x = 13 11. ¤BEC § ¤ECB 15. 70 17. 70 19. 17.5 21. 81 and 81 23. 65 25. 3