4.5 what information do i need? pg. 19 more conditions for triangle similarity
TRANSCRIPT
4.5
What Information Do I Need?
Pg. 19More 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
AB
DE
AC
DF A D
Included AngleAngle 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 – FLOWCHARTSLynn 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.
36
=12
= 12
816
ΔABC ~
SAS~
given given given
B ≅ ∠L
ΔKLM
4.38 – USING SIMILARITYExamine 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
GC
E
F25°
25°60°20
36
15 27 36
1527
= 59
20.
36= 5
9
ΔGCD ~
SAS~
given Reflexive given
C ≅ ∠C
ΔFCE
C
D
GC
E
F25°
25°60°20
36
15 27 36
Both are correct!
c. Find all the missing side lengths and all the missing angle measures in the two triangles.
C
D
GC
E
F
25°25°
60°2036
15 27 36
60°95°
95°
15
27 36
x
27x = 540x = 20
x
4.39 – FLOWCHARTSDetermine if the triangles are similar. If they are, state your reasoning.
31°
no
Yes, SAS~
24
16
3
2
36
28
9
7
no
Yes, AA~
10
4
5
2
15
6
5
2
Yes, SAS~
no
no
71°
38°71° 71°
Yes, AA~
no
two correspondingIf _____ __________________angles are _________, then the triangles are similar by AA~.
equal
If _________ ____________________ sides are _______________________, then the triangles are similar by SSS~.
three corresponding
proportional
2
3
4
4
6
8
If _____ _____________________ sides are _________________and the angle _______________
them is ____________, then the triangles are similar by SAS~.
two corresponding
proportional between
equal
2
3
4
6