<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
Dismiss
Skip Navigation
Our Terms of Use (click here to view) and Privacy Policy (click here to view) have changed. By continuing to use this site, you are agreeing to our new Terms of Use and Privacy Policy.

9.5: Similar Triangles Review

Difficulty Level: At Grade Created by: CK-12

[Editor’s note: This day is set aside for a quiz and a review of similar triangles.]

Learning Objectives

  • Review the concepts of angle congruence and segment proportionality in similar triangles.

Chords

Remember from lesson 2: a chord is a line segment that has both endpoints on a circle.

  • Line segments whose endpoints are both on a circle are called _______________.

Segments of Chords Theorem

If two chords intersect inside a circle so that one chord is divided into segments of lengths a and b and the other into segments of lengths c and d, then the segments of the chords satisfy the following relationship:

ab=cd

This means that the product of the segment lengths of one chord equals the product of the segment lengths of the second chord:

  • The intersection point splits each ______________________ into two segments.
  • The product of both segment lengths of one chord is ____________________ to the product of both segment lengths of the other chord.

We prove this theorem on the following page.

Proof

We connect points A and C and points D and B to make ΔAEC and ΔDEB:

Statements Reasons
1. AECDEB 1. Vertical angles are congruent
2. CABBDC 2. Inscribed angles intercept the same arc
3. ACDABD 3. Inscribed angles intercept the same arc
4. ΔAECΔDEB 4. AA similarity postulate
5. cb=ad 5. In similar triangles, the ratios of corresponding sides are equal.
6. ab=cd 6.Cross multiplication

Example 1

Find the value of the variable x:

Use the products of the segment lengths of each chord:

10x10xx=812=96=9.6

Reading Check:

1. In your own words, define a chord.

2. True or false: When two chords intersect inside a circle, the sum of the segment lengths of one chord is equal to the sum of the segment lengths of the other chord.

3. How could you change the statement in #2 above to make it true?

4. In the space below, make up your own problem with two chords that intersect inside a circle, and then solve your problem.

(Hint: if you are having trouble, look at Example 1 on the previous page and model your problem after that one.)

My Notes/Highlights Having trouble? Report an issue.

Color Highlighted Text Notes
Show More

Image Attributions

Show Hide Details
Description
Authors:
Grades:
8 , 9 , 10
Date Created:
Feb 23, 2012
Last Modified:
May 12, 2014
Save or share your relevant files like activites, homework and worksheet.
To add resources, you must be the owner of the section. Click Customize to make your own copy.
Please wait...
Please wait...
Image Detail
Sizes: Medium | Original
 
Here