Loading...

How well do you understand the concepts and skills introduced in this lesson?

Are you ready to take this lesson's quiz? The questions below will help you find out. Make sure you understand why each answer is correct—if you don't, review that part of the lesson.

What is an isosceles triangle?

  1. A triangle with no equal side lengths.

  2. A triangle with three equal side lengths.

  3. A triangle with three interior angles less than \(90^\circ\).

This type of triangle is scalene.

Isosceles triangles have two side lengths that are equal.

This type of triangle is equilateral.

This is an acute triangle.

What type of triangle is this?

A triangle with angle measurements of 35.184 degrees, 13.325 degrees, and 131.491 degrees. The sides of the triangle measure 5 cm, 2 cm, and 6.5 cm.

  1. obtuse isosceles triangle

  2. acute scalene triangle

  3. acute equilateral triangle

An isosceles triangle has two side lengths that are equal.

An acute triangle has three interior angles less than \(90^\circ\).

This triangle has one obtuse angle with three sides that are not equal.

An acute equilateral triangle has three interior angles less than \(90^\circ\) and three side lengths that are all equal.

Which side lengths cannot be used to construct a triangle?

  1. \(0.2\ \text{in}.,\ 0.3\ \text{in}.,\ 0.3\ \text{in}.\)

  2. \(12.5\ \text{cm},\ 9.2\ \text{cm},\ 5.3\ \text{cm}\)

  3. \(47.7\ \text{ft},\ 32.9\ \text{ft},\ 28.3\ \text{ft}\)

The triangle inequality theorem states that any type of triangle can exist if the sum of two side lengths is greater than the third side length. This is true here. Look for three side lengths such that when two of them are added, the sum is less than the third.

The triangle inequality theorem states that any type of triangle can exist if the sum of two side lengths is greater than the third side length. This is true here. Look for three side lengths such that when two of them are added, the sum is less than the third.

The triangle inequality theorem states that any type of triangle can exist if the sum of two side lengths is greater than the third side length. This is true here. Look for three side lengths such that when two of them are added, the sum is less than the third.

Since \(2.3\ \text{in}.\ +\ 1.7\ \text{in}.\ \lt\ 4.6\ \text{in}.\), this triangle cannot exist, which implies it cannot be constructed.

Which interior angle measurements can be used to construct a triangle?

  1. \(90^\circ,\ 80^\circ,\ 70^\circ\)

  2. \(21^\circ,\ 88^\circ,\ 75^\circ\)

  3. \(80^\circ,\ 45^\circ,\ 35^\circ\)

A triangle can only be constructed when its interior angles add up to \(180°\). \(90^\circ\ +\ 80^\circ\ +\ 70^\circ\ =\ 240^\circ\)

A triangle can only be constructed when its interior angles add up to \(180^\circ\). \(67^\circ\ +\ 104^\circ\ +\ 9^\circ\ =\ 180^\circ\).

A triangle can only be constructed when its interior angles add up to \(180^\circ\). \(21^\circ\ +\ 88^\circ\ +\ 75^\circ\ =\ 184^\circ\).

A triangle can only be constructed when its interior angles add up to \(180^\circ\). \(80^\circ\ +\ 45^\circ\ +\ 35^\circ\ =\ 160^\circ\).

A triangular roof is to be constructed. What are possible side lengths and angle measurements for this roof?

  1. Side Lengths: \(14\ \text{ft}.,\ 19\ \text{ft}.,\ 31\ \text{ft}.\)

    Angle Measurements: \(46^\circ,\ 58^\circ,\ 79^\circ\)

  2. Side Lengths: \(12\ \text{ft}.,\ 22.5\ \text{ft}.,\ 35.5\ \text{ft}.\)

    Angle Measurements: \(34^\circ,\ 45^\circ,\ 101^\circ\)

  3. Side Lengths: \(1.5\ \text{ft}.,\ 7\ \text{ft}.,\ 9\ \text{ft}.\)

    Angle Measurements: \(11^\circ,\ 98^\circ,\ 61^\circ\)

A triangle can only exists if the angle measurements inside it equal \(180^\circ\). \(46^\circ\ +\ 58^\circ\ +\ 79^\circ\ =\ 183^\circ\).

A triangle can only exists if two sides, when added, are greater than the third side. Here, \(12\ \text{ft}\ +\ 22.5\ \text{ft}\ =\ 34.5\ \text{ft}\), which is less than \(35.5\ \text{ft}\).

A triangle can only exists if two sides, when added, are greater than the third side. Here, \(1.5\ \text{ft}\ +\ 7\ \text{ft}\ =\ 8.5 \text{ft}\), which is less than \(9\ \text{ft}\). Also, the angle measurements inside a triangle must always equal \(180^\circ\); they do not equal that here.

By using the triangle inequality theorem and sum theorem, it can be determined that this triangle can be constructed.

Summary

Questions answered correctly:

Questions answered incorrectly: