4.5 What Information Do I Need? Pg. 19 More Conditions for Triangle Similarity

4.5 – What Information Do I Need? More Conditions for Triangle Similarity So far, you have worked with two methods for determining that triangles are similar: AA~ and SSS~. Are these the only ways to determine if two triangles are similar? Today you will investigate similar triangles and complete your triangle similarity conjectures.

Side-Angle-Side Similarity: A B C D E F If all 2 corresponding sides are proportional and the included angle is equal, then the triangles are similar

Included Angle Angle where the two sides meet

4.35 – ASS~ OR SSA~ What if the angle isn’t the included angle in the sides? Can it still make similar shapes?

There is no ASS in geometry!

4.36– ANYTHING ELSE? What other triangle similarity conjectures involving sides and angles might there be? List the names of every other possible triangle similarity conjecture you can think of that involves sides and angles. AAA~AAS~ ASA~ SAA~ SSA~ SAS~ ASS~ SSS~

b. Go through your list of possible triangle similarity conjectures, crossing off all the invalid ones and all the ones that contain unnecessary information. AAA~ AAS~ ASA~ SAA~ SSA~ SAS~ ASS~ SSS~

c. How many valid triangle similarity conjectures are there? List them. AAA~ AAS~ ASA~ SAA~ SSA~ SAS~ ASS~ SSS~ 3 AA~SSS~SAS~

4.37 – FLOWCHARTS Lynn wants to show that the triangles are similar. a. What similarity conjecture should Lynn use? SAS~ Two sides and included angle

b. Make a flowchart showing that these triangles are similar.

3636 = 1212 = ΔABC ~ SAS~ given ΔKLM

4.38 – USING SIMILARITY Examine the triangles. a. Are these triangles similar? If so, make a flowchart justifying their similarity. Hint: It might help to draw the triangles separately first.

C D G C E F 25° 60° = = 5959 ΔGCD ~ SAS~ givenReflexive given ΔFCE

C D G C E F 25° 60° Both are correct!

c. Find all the missing side lengths and all the missing angle measures in the two triangles. C D G C E F 25° 60° ° 95° 27x = 540 x = 20 x

4.39 – FLOWCHARTS Determine if the triangles are similar. If they are, state your reasoning.

31° no

Yes, SAS~

no

Yes, AA~

Yes, SAS~

no

71° 38° 71° Yes, AA~

no

twocorresponding If _____ __________________angles are _________, then the triangles are similar by AA~. equal

If _________ ____________________ sides are _______________________, then the triangles are similar by SSS~. threecorresponding proportional

If _____ _____________________ sides are _________________and the angle _______________ them is ____________, then the triangles are similar by SAS~. twocorresponding proportional between equal