D-3 Isosceles Triangle Thm and Converse HW Name______________________

Geometry

1) Determine whether each statement is always, sometimes, or never true. Justify each conclusion with an

explanation and/or diagram(s).

a) The largest angle of an isosceles triangle is obtuse.

b) If a right triangle has a 45 angle, then it is isosceles.

2) Draw a picture of each situation and give the measure of the THREE angles of each triangle described below.

a) An isosceles triangle with a vertex angle of 70.

b) An isosceles triangle with a base angle of 70.

c) An isosceles triangle which the vertex angle is twice the measure of the base angles.

3) Label the diagram below if ABF is isosceles, CDF is equilateral, and mAFD = 150. Then find each angle

listed below.

mCFD = ______

mAFB = ______

mA = ______

mABF = ______

4) Knowing the converse of the Isosceles Triangle Theorem, would triangle ABC be scalene, equilateral, or scalene

if two of the angles measure 38 degrees and 85 degrees? Explain your reasoning.

***These are a little tough 😊 …Remember the Isos. Triangle thm, its converse, and triangle sum thm.

5) Determine the value of x for each of the following situations.

a) x = _______ b) x = ______

c) x = ______ d) x = ______

e) x = _______ f) Find x and y ☺ x = ______ y = ______

72

9x

(8y – 16)

g) If 𝐵𝐶 ̅̅ ̅̅ ̅ ≅ 𝐵𝐴̅̅ ̅̅ , find mB. mB = _____ h) Find the perimeter of STV. P= _________