Download 4.7 Using Isosceles and Equilateral Triangles

Mathematician: _________________________
Date: _______________
Core-Geometry: 4.7 Isosceles &
Equilateral Triangles
Warm-up:
1. Solve:
(a) x = 3
(b) 3x - 2 = 2
2. Write, in slope-intercept form, the equation of the line through (1, -2)
with slope m = -3.
Review
1.
2. Write a congruence statement for each pair of figures:
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4.7 Using Isosceles and Equilateral Triangles
A triangle is isosceles if it has at ________________ two ___________________
sides. When an ___________________ triangle has exactly two
__________________ sides, these two sides are the _________of the triangle. The
angle formed by the _____________ is called the ______________ angle. The third
side is called the ________ of the isosceles triangle. The _________adjacent angles
to the base are called ___________ angles.
Another special relationship exists. If two ________of a triangle are
_______________, then the angles _____________________ are congruent.
The converse is also true. If ______angles of a ______________are
_______________then the _______________opposite them are _______________.
Example 1
Find the missing measures below.
Example 2
Write an algebraic equation and solve for the variables for the triangles below.
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Remember that an equilateral triangle has ________ congruent _________________.
By applying what we know about two congruent sides, if a triangle is
_____________________ then it is also __________________________. The
converse is also true. If a triangle is ___________________________ then it is also
__________________________.
Example 3
Find the values of x and y if 𝑚∡𝐷𝐸𝐹 = 90˚.
Example 4
Find the value of x.
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Example 5: Is an isosceles triangle always an acute triangle? Explain.
Hmwk 3.5
p.267 Ex 4.7 # 3-6 (no need to name the theorem used), 7-13, 15-17, 19, 30
p.286 Chapter 4 test # 1-10, 12
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