3.3 Inequalities in one Triangle

3.3 Inequalities in one Triangle

Inequalities in One Triangle

We have covered many of the basic features of triangles so far. Now we will think just a little about the implications of those basic properties of triangles before we move on to advanced triangle concepts in unit 4.

First...just making sure that we know what an inequality is. Its when something is bigger and something is smaller, in case you were wondering.

The comparison property just reminds us that there are only 3 possible relationships between 2 numbers. The Transitive property should be familiar by now, and the other two tell us that if we add or subtract the same amount from an inequality, the relationship stays the same.

Makes sense, right? The exterior angle is equal to the sum of the two remote interior angles, so it MUST be bigger than either of them on their own.

This makes sense as well... the sides of a triangle are controlled by the angle OPPOSITE from each side. The bigger the angle, the longer the opposite side.

Multiple Choice

List the SIDES from smallest to largest.

• $\overline{PR},\ \overline{QP},\ \overline{RQ}$

• $\overline{PR},\ \overline{RQ},\ \overline{QP}$

• $\overline{QP},\ \overline{PR},\ \overline{RQ}$

• $\overline{QP},\ \overline{RQ},\ \overline{PR}$

Multiple Choice

Find the largest angle in Δ PRQ

• ∠R
• ∠P
• ∠Q
• ∠S

Multiple Choice

Name the sides from SMALLEST to LARGEST

• RS, ST, TR
• ST, RT, RS
• RT, ST, RS
• RT, RS, ST

Multiple Choice

Find the measure of the indicated angle.

• 145 degrees

• 24 degrees

• 20 degrees

• 21 degrees

Multiple Choice

Where would the largest angle of a triangle be located?

• Across from the longest side.
• Across from the shortest side
• I need more information to get an answer.

Multiple Choice

Name the angles from SMALLEST to LARGEST

• Q, R, P
• P, Q, R
• R, P, Q
• R, Q, P

Multiple Choice

Order the sides from greatest to least

• a , b , c

• b , c , a

• c , b , a

• a , c , b

Multiple Choice

The smallest angle would be located where in a triangle?

• Across from the smallest side.
• Across from the largest side
• Cannot tell

Multiple Choice

Name the largest angle in this triangle.

• ∠D
• ∠E
• ∠F

Multiple Choice

Name the smallest angle in this triangle.

• ∠A

• ∠B

• ∠C

Open Ended

Open Ended

(We will discuss how to find the exact measurement of that side in unit 4 :-) )

Open Ended

Open Ended