Become a math whiz with AI Tutoring, Practice Questions & more.
When we start drawing lines in circles, a few interesting things start to happen. One of the patterns we may notice is the creation of angles in the center of the circle. These angles follow very specific rules, and one of these is highlighted by the angles of intersecting chords theorem. But what is this theorem really about? Let's find out:
The angles of intersecting chords theorem states that:
Let's back up for a moment here and define a few terms:
It helps if we can visualize all of this taking shape. Consider the following circle:
As we can see, there are four angles formed by the two intersecting chords: PR and RS. There are also two arcs shaded in red: and .
If we were to put the intersecting chords theorem into a formula, it would look something like this:
Remember, vertical angles are congruent -- which means that their measures are equal. This means that angle 1 is congruent to angle 3, and angle 2 is congruent to angle 4.
Let's take another look at that circle:
If degrees and degrees, then can we find the measure of angle 3?
We know that:
Let's plug in our values:
Now we know that angle 3 equals 101 degrees!
Common Core: High School - Geometry Flashcards
Common Core: High School - Geometry Diagnostic Tests
Advanced Geometry Diagnostic Tests
The angles of intersecting chords theorem is just one of many geometrical theorems to keep track of. A qualified tutor can provide your student with plenty of tips and tricks to memorize these theorems. Students can also ask plenty of questions in a 1-on-1 environment that they might not have a chance to raise in class time. Contact Varsity Tutors, and we'll match your student with a tutor.