Understanding the Angle-Side Theorem in Triangles

The video tutorial explains the angle-side theorem, which states that in a triangle, the longest side is opposite the largest angle, and the shortest side is opposite the smallest angle. It provides examples to illustrate how to calculate missing angles and determine the longest side based on given angles and side lengths. The tutorial also covers scenarios where triangles have equal longest sides, explaining how to identify the corresponding largest angles.

What does the angle-side theorem state about the relationship between angles and sides in a triangle?

• The shortest side is opposite the largest angle.

• The longest side is opposite the smallest angle.

• All sides are equal in length.

• The longest side is opposite the largest angle.

In a triangle with angles 35°, 110°, and 35°, which side is the longest?

• All sides are equal.

• The side opposite the 35° angle.

• The side opposite the 110° angle.

• The side opposite the 90° angle.

What is the sum of the angles in any triangle?

• 270 degrees

• 360 degrees

• 180 degrees

• 90 degrees

If two angles in a triangle are 35° and 110°, what is the measure of the third angle?

• 65°

• 35°

• 45°

• 55°

If a triangle has side lengths of 4, 8, and 6, which angle is the largest?

• The angle opposite the side of length 4.

• The angle opposite the side of length 6.

• The angle opposite the side of length 8.

• All angles are equal.

In a triangle with two sides of equal length, what can be said about the angles opposite these sides?

• They are different.

• They are equal.

• One is larger than the other.

• They are both right angles.

In a triangle with sides 8, 8, and 6, which angles are the largest?

• The angles opposite the sides of length 8.

• The angles opposite the sides of length 6.

• All angles are equal.

• The angles opposite the sides of length 7.