Angles Formed by Intersecting Chords Worksheets for High School Geometry

📚 Topic Summary

When two chords intersect inside a circle, they form angles. The measure of each angle is half the sum of the measures of the intercepted arcs. Let's say chords $AC$ and $BD$ intersect at point $E$ inside the circle. Then, the measure of angle $\angle AEB$ (and its vertical angle $ \angle CED$) is given by: $\frac{1}{2}(m\stackrel{\frown}{AB} + m\stackrel{\frown}{CD})$. Similarly, the measure of angle $ \angle AED$ (and its vertical angle $ \angle BEC$) is given by: $\frac{1}{2}(m\stackrel{\frown}{AD} + m\stackrel{\frown}{BC})$. Remember, the intercepted arcs are the arcs 'cut off' by the angles.

This worksheet will help you practice using this important theorem. Let's get started!

📐 Part A: Vocabulary

Match the terms on the left with their definitions on the right:

1. 1. Chord
2. 2. Intercepted Arc
3. 3. Circle
4. 4. Angle
5. 5. Vertex

1. A. The point where two rays meet to form an angle.
2. B. The set of all points equidistant from a center point.
3. C. The arc that lies in the interior of an angle.
4. D. A straight line segment whose endpoints both lie on the circle.
5. E. The figure formed by two rays sharing a common endpoint.

✍️ Part B: Fill in the Blanks

Complete the paragraph using the words provided: chords, half, intercepted arcs, angle, sum.

When two _______ intersect inside a circle, they create an _______. The measure of this angle is _______ the _______ of the measures of the _______.

🤔 Part C: Critical Thinking

Explain in your own words why it is important to know the measures of the intercepted arcs when finding the measure of an angle formed by intersecting chords.