Isosceles Triangles

Triangle ABC is an isosceles right triangle. What is the measure of a base angle?

45°

Triangle XYZ is isosceles. The measure of the vertex angle, Y, is twice the measure of a base angle. What is true about triangle XYZ? Check all that apply.

Angle Y is a right angle. The measure of angle Z is 45° The perpendicular bisector of XZ creates two smaller isosceles triangles.

Triangle SQT is isosceles. The measure of angle STQ is 48°. What is the measure of <STR?

a. 24°

Triangle KNM is isosceles, where angle N is the vertex. What is the measure of angle K?

b. 25

Isosceles triangle ABC has a perimeter of 96 centimeters. The base of the triangle is AC and measures 24 centimeters. What is the measure of AB?

b. 36 cm

The vertex angle of an isosceles triangle measures 40°. What is the measure of a base angle?

b. 70°

What is always true about the angles of an isosceles triangle?

b. At least two of the angles are congruent.

Triangle ABC is shown below. What is the length of line segment AC?

c. 14

Triangle ABC is isosceles. What is the length of BC?

c. 40

Right triangle ABC is isosceles and point M is the midpoint of the hypotenuse. What is true about triangle AMB?

c. It is an isosceles right triangle.

Consider the diagram and proof by contradiction. Given: ABC with AB ~= AC (Since it is given that AB ~= AC, it must be true that AB = AC. Assume <B and <C are not congruent.) Therefore, it can be concluded that _______.

b. <B ~= <C

GJ bisects <FGH and is a perpendicular bisector of FH. What is true of triangle FGH?

d. It has exactly 3 congruent sides.

RT is a perpendicular bisector of UV. What is true of any triangle created by points U, V, and any point on RT other than S?

d. It will be an isosceles triangle.