GeoGebra Classroom

# Opposite Sides and Angles Theorem

Please notice that each angle and its opposite side (the side not touching the angle) are the same color. We are now going to explore some relationships that angles have to their opposite sides, and relationships that sides have to their opposite angles.

## Opposite Sides & Angles Theorem

Move the vertices of the triangle to make the RED ANGLE the largest angle. Which SIDE is the longest?

Select all that apply
• A
• B
• C
Check my answer (3)

Move the vertices of the triangle to make the GREEN ANGLE the largest angle. Which SIDE is the longest?

Select all that apply
• A
• B
• C
Check my answer (3)

Move the vertices of the triangle to make the BLUE ANGLE the smallest angle. Which SIDE is the shortest?

Select all that apply
• A
• B
• C
Check my answer (3)

Move the vertices of the triangle to make the BLUE SIDE the biggest side. Which ANGLE is the biggest?

Select all that apply
• A
• B
• C
Check my answer (3)

Move the vertices of the triangle to make the GREEN SIDE the biggest side. Which ANGLE is the biggest?

Select all that apply
• A
• B
• C
Check my answer (3)

Move the vertices of the triangle to make the RED SIDE the shortest side. Which ANGLE is the smallest?

Select all that apply
• A
• B
• C
Check my answer (3)

Move the vertices of the triangle to make the BLUE SIDE the shortest side. Which ANGLE is the smallest?

Select all that apply
• A
• B
• C
Check my answer (3)

## LET'S SUMMARIZE!!

The BIGGEST ANGLE lies opposite the _____ SIDE.

Select all that apply
• A
• B
• C
Check my answer (3)

## LET'S SUMMARIZE!!

The SMALLEST ANGLE lies opposite the _____ SIDE.

Select all that apply
• A
• B
• C
Check my answer (3)

## LET'S SUMMARIZE!!

The MIDDLE ANGLE lies opposite the _____ SIDE.

Select all that apply
• A
• B
• C
Check my answer (3)

## LET'S SUMMARIZE!!

The BIGGEST SIDE lies opposite the _____ ANGLE.

Select all that apply
• A
• B
• C
Check my answer (3)

## LET'S SUMMARIZE!!

The MIDDLE SIDE lies opposite the _____ ANGLE.

Select all that apply
• A
• B
• C
Check my answer (3)

## LET'S SUMMARIZE!!

The SMALLEST SIDE lies opposite the _____ ANGLE.

Select all that apply
• A
• B
• C
Check my answer (3)
PLEASE VIEW THE ANSWERS OF THE SUMMARIZATION AND WRITE THESE 6 STATEMENTS DOWN IN YOUR NOTES!!

## Use the information from the summary to fill in the blank.

In , if <Z is the smallest angle, then ___ is the smallest side.

## Use the information from the summary to fill in the blank.

In , if <Y is the smallest angle, then ___ is the smallest side.

## Use the information from the summary to fill in the blank.

In , if YZ is the biggest side, then ___ is the biggest angle.

## Use the information from the summary to fill in the blank.

In , if MS is the biggest side, then ___ is the biggest angle.

## Use the information from the summary to fill in the blank.

In , if <S is the biggest angle, then ___ is the biggest side.

In ΔHKJ, m∠K =125º, m∠H =11º andHJ = 8 in. a.﻿ What is m∠J? b. Is KJ =, <, or > 8 in.? ﻿c. Is HK =, <, or > 8 in?

11. In ΔDEF, m∠D =80º, m∠E =60º ,DE = 5 in, and ﻿EF = 8 in. ﻿a) What is m∠F?﻿ ﻿b) List the angles in ΔDEF in order from smallest to largest. ﻿c) List the sides of ΔDEF in order from shortest to longest.﻿ ﻿d) The length of DF has to greater than ___ and less than ___.

12. In ΔPQR﻿, PQ = 18m, QR = 26m, and PR = 18.5m. List the angles of ΔPQR in order from smallest to largest.