Try It

Triangle Classification and Angle Theorems Practice

Practice Problems

  1. Select the isosceles right triangle
    1. A Triangle • Two sides have one tick mark on them. • The third side has no marks. • The triangle has one angle measuring more than 90 degrees.
    2. A Triangle • Three sides have one tick mark on them.
    3. A Triangle • There are no tick marks on any of the segments. • The triangle has one angle measuring more than 90 degrees.

    Answer: a. A Triangle • Two sides have one tick mark on them. • The triangle has a box to indicate the measure of one its angles.

  2. Select the equilateral triangle
    1. A Triangle • Two sides have one tick mark on them. • The triangle has a box to indicate the measure of one its angles.
    2. A Triangle • Three sides have one tick mark on them.
    3. A Triangle • There are no tick marks on any of the segments. • The triangle has one angle measuring more than 90 degrees.

    Answer: b. A Triangle • Three sides have one tick mark on them.

  3. Select the scalene obtuse triangle
    1. A Triangle • Two sides have one tick mark on them. • The triangle has a box to indicate the measure of one its angles.
    2. A Triangle • Three sides have one tick mark on them.
    3. A Triangle • There are no tick marks on any of the segments. • The triangle has one angle measuring more than 90 degrees.

    Answer: c. A Triangle • There are no tick marks on any of the segments. • The triangle has one angle measuring more than 90 degrees.

    4. Questions 4 - 6 refer to this image:
    Traingle RST • Segments ST and RT both have one tick marks on them. • The third side, segment SR, has no tick marks. • Angles RST and SRT both measure 65 degrees. • Angle RTZ is an exterior angle of the triangle.

  4. m∠RTS = ______
    1. 180°
    2. 50°
    3. 65°
    4. 130°

    Answer: b. 50°

  5. m∠RTZ = ______
    1. 180°
    2. 20°
    3. 65°
    4. 130°

    Answer: d. 130°

  6. Classify triangle RST in relation to its angles.
    1. acute
    2. right
    3. obtuse
    4. equiangular

    Answer: a. acute

  7. Solve for y = ___.
    This is a triangle with two congruent sides. There is a segment drawn from the vertex angle and perpendicular to the base. The perpendicular segment forms two right triangles inside of the triangle. In the left interior triangle, the measure of one acute angle is y degrees. In the right interior triangle, the measure of one acute angle is 47 degrees.
    1. 45°
    2. 90°
    3. 86°
    4. 43°

    Answer: d. 43°

  8. FJH is an equilateral triangle. Find x and y.
    Triangle HJF. JH = 3x minus 8. HF = 2y minus 1. The measure of angle H = 4y minus 4 degrees.
    1. x = 7/5, y = 16
    2. x = 7, y = 16
    3. x = 7/5, y = 14
    4. x = 7, y = 14

    Answer: b. x = 7, y = 16

  9. Use the Interior Angle Sum Theorem to solve for x. Then evaluate each angle in order to classify the triangle as acute, right, or obtuse if ...
    ∠1 = x + 2
    ∠2 = 5x
    ∠3 = 5x + 2
    1. x = 16; acute triangle
    2. x = 17; obtuse triangle
    3. x = 16; right triangle
    4. x = 18; right triangle

    Answer:a. x = 16; acute triangle

  10. Find m∠K
    Triangle LKM; The measure of angle L is 4x plus 7 degrees; The measure of angle K is 6x minus 9; The measure of an exterior angle to triangle LKM is 118 degrees; The exterior angle's name is angle LMN.
    1. 63°
    2. 55°
    3. 79°
    4. 39°

    Answer: a. 63°