in this unit, you will learn: how to support a mathematical statement using flowcharts and...
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Triangle Similarity
Use a flow proof to prove similarity.
Use a flow proof to prove similarity.
In this unit, you will learn: How to support a mathematical statement using flowcharts and conditional statements. About the special relationships between shapes that are similar or congruent. How to determine if triangles are similar or congruent. 3.1 Prove Triangle Similarity I can prove two triangles are similar. G.3.B, G.1.F This means I can Use a flow chart, two-column proof, or paragraph proof to demonstrate the steps needed to
prove that two triangles are similar Determine if two triangles are similar using triangle similarity conjectures (AA~, SAS~, SSS~) CPM Materials: 3.2.1 - 3.2.6 Will need extra practice State EOC Examples: For a given ∆RST, prove that ∆XYZ, formed by joining the midpoints of the sides of ∆RST, is
similar to ∆RST. .
Unit 3 Triangle Similarity Planned Teaching Window: 10/10/11 - 10/21/11
Similar figures have the SAME SHAPE.
Corresponding sides are PROPORTIONAL.
What does it mean to be similar?
Same SHAPE…right?How can you tell if they are the same shape?
Corresponding angles are equal. Corresponding sides are proportional.
How can we tell if triangle are similar?
AA stands for "angle, angle" and means that the triangles have two of their angles equal.
If two triangles have two of their angles equal, the triangles are similar.
AA or angle-angle
For example, these two triangles are similar:
AA similarity If two of their angles are
equal, then the third angle must also be equal, because angles of a triangle always add to make 180°.
In this case the missing angle is:
180° - (72° + 35°) = 73°.
So AA could also be called AAA.
SSS stands for "side, side, side" and means that we have two triangles with all three pairs of corresponding sides in the same ratio (proportional).
For example:
SSS or side-side-side
If two triangles have three pairs of sides in the same ratio, then the triangles are similar.
In this example, the ratios of sides are:
a: x = 6 : 7.5 =12:15 = 4 : 5 or 0.8
b: y = 8 : 10 = 4 : 5 or 0.8
c: z = 4 : 5 or 0.8
These ratios are all equal, so the two triangles are similar.
Practice / ReviewChapter 3
Problems 45-46, 48-52
Day 2Similar? Why or why not?
Why ASS does not always work.
Proof Video Clip
Exploring a Flow Proof
Ch. 3 (53-55, 57,59-63)
Check your answers in your group.Any troubles, write the # on the board.
Practice / Review
1) Angle-Angle similarity (AA~)2) Side-Side-Side similarity (SSS~)
Now you know 2 ways to show that triangles are similar (the same shape):
How can you tell if two triangles are the same shape (similar) and SIZE?
If they are the same shape and same size, we say they are CONGRUENT.
Ch. 3 (64, 66-67 in class & 68-72)
Practice / Review
Ch. 3 (64, 66-67 in class & 68-72)Write the “problem” problems on the board.
Go over HW with your team.
SAS stands for "side, angle, side" and means that we have two triangles where:◦the ratio between two sides is the same as
the ratio between another two sides
◦and we we also know the included angles are equal.
SAS
If two triangles have two pairs of sides in the same ratio and the included angles are also equal, then the triangles are similar.
SAS
Ch. 3 (74-76, 78-82)
Practice / Review
Ch. 5(94-100)
Go over HW with Team