Transcript 2.3.1 What information do I need?

2.3.1 What
information do
I need?
October 5, 2015
Objectives
• CO: SWBAT determine if
triangles are similar.
• LO: SWBAT explain how they
know that the triangles are
similar.
2-72. Kendall wanted to investigate if he could prove two triangles were similar
without knowing if any of the corresponding angles were congruent. That, is,
he wanted to test whether SSS ~ is a triangle similarity condition.
a.
b.
Before experimenting, make a
prediction. Do you think that two
triangles must be similar if all three
pairs of corresponding sides lengths
have the same ratio? Write down
your prediction and share it with your
teammates.
Experiment with Kendall’s idea. To
do this, use the eTools below to test
triangles with proportional side
lengths. Begin with the side lengths
listed below, then try some
others. Can you create two triangles
with proportional side lengths that
are not similar? Investigate, sketch
your shapes, and write down your
conclusion.
o (1/4) Triangle #1: side lengths 3, 5, 7
Triangle #2: side lengths 6, 10, 14
• http://tinyurl.com/math2-72b1
o (2/3) Triangle #1: side lengths 3, 4, 5
Triangle #2: side lengths 6, 8, 10
• http://tinyurl.com/math2-72b2
o When the sides are proportional,
then the triangles are similar.
2-73. Robel’s team is using the SAS ~ and SSS ~ conditions to show that two triangles
are similar. “This is too much work,” Robel says. “When we’re using the AA ~ condition, we
only need to look at two pairs of corresponding parts. Let’s just calculate the ratios for two pairs
of corresponding sides to determine that triangles are similar.”
• If two pairs of corresponding side lengths have the
same ratio, must the triangles be similar? That is, is
SS ~ a valid similarity condition? If not, what
additional information is needed?
o There is more than one option for the third side (a – b < c < a + b), two
sides is not enough information.
2-74. TESTING MORE SIMILARITY CONDITIONS
• Cori’s team put “SSA ~” on their list of possible
triangle similarity conditions. To test their idea, Cori
started by drawing a triangle.
a. Use to investigate whether SSA ~ is a valid triangle similarity condition. If a
triangle has two side lengths proportional to 4 cm and 5 cm, and has the
same angle that is not between those sides, must it be similar to Cori’s
triangle? In other words, can you create a triangle that is not similar to
Cori’s? Tool
If you determine SSA ~ is not a valid similarity condition, cross it off your
list!
b. Kashi asks, “I want to test ASA~, which means I start with two pairs of
congruent angles, and the lengths of the sides connecting these angles
are proportional. Would that be enough to know the triangles are
similar?” Discuss this with your team and write Kashi an explanation.
It is the same as AA~ with more work.
32 + 52 + m<P = 180
m<P = 96
Yes, they are similar
by AA~
∆𝐽𝑃𝑂~∆𝑋𝑉𝐾
14
20
=
44.8 64
.3125 = .3125
Yes, they are similar
by SAS~
∆𝑇𝑄𝑈~∆𝐼𝐾𝐹
<A ≅ <A (Reflexive Prop)
Yes, they are similar by
AA~
∆𝑀𝑁𝐻~∆𝑀𝑆𝐿
18
90
44
202.4
58.5
?
211.2
=
=
.2 ≠ .217… ≠ .2769…
No, they are not
similar by SSS~