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Transcript
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: 1 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. 2 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 πβ‘π·πΈπΉ = 90Λ. Example 4 Find the value of x. 3 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 4