Download it is an isosceles triangle. +

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Do Now

Take out your compass and a protractor.

Look at the new seating chart and find your new seat.

Classify this triangle:


By angles

By side lengths
On a piece of paper draw a triangle. (It can be acute, right, or
obtuse.) Make it big enough to measure the angles.
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Isosceles Triangles
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TODAY’S OBJECTIVES

Discover the relationship between the base angles of an
isosceles triangle.

Explain the sum of the measures of the angles of a triangle.

Write a paragraph proof.

Use problem solving skills.
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YOU MAY ASSUME THAT…

Lines are straight

If two lines intersect, they intersect at a point.
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DO NOT ASSUME THAT…

Lines are parallel unless they are marked parallel, even if
they “look” parallel

Lines are perpendicular unless they are marked
perpendicular, even if they “look” perpendicular

Pairs of angles, segments, or polygons are congruent unless
they are marked congruent, even if they “look” congruent.
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The triangle sum: Investigation

On a piece of paper, draw a triangle. (Make sure your group
has at least one obtuse and one acute triangle.)

Measure all three angles as accurately as possible.

Find the sum of the measures of the three angles. Compare
with your group.

Mark your angles A, B, and C. Cut out the triangle.

Tear off the three angles. Arrange them so their vertices
meet at a point. How does this arrangement show the sum of
the angle measures?
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Triangle Sum Conjecture

The sum of the measures of the angles in every triangle
is___.

180o .

Based on what type of reasoning?

Inductive.

Can we prove it using deductive reasoning?

Let’s prove it!
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Proof of Triangle Sum Conjecture

As a group, explain why the Triangle Sum Conjecture is true
by writing a paragraph proof (a deductive argument that
uses written sentences to support its claims with reasons).

Hints to get started:

What are you trying to prove?

How are the angles related?

Mark your diagram.

How can you use the information you have to prove that the
Triangle Sum Conjecture is true for every triangle?

Remember what you can and cannot assume.
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Practice

Solve for p and q.
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Properties of Isosceles Triangles

Two sides are congruent
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Base Angles in an Isosceles
Triangle: Investigation
1.
Draw an angle. Label it C. This will be the vertex angle of
your isosceles triangle.
2.
Place a point A on one ray. Using your compass, copy
segment CA onto the other ray and mark point B so that
CA=CB.
3.
Draw AB.

How do you know ΔABC is isosceles?

Name the base and the base angles.

Use your protractor to measure the base angles. What do you
notice?
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Isosceles Triangle Conjecture

If a triangle is isosceles, then ____________________________.

it’s base angles are congruent.

Is the converse true?

Let’s find out.
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Converse: Investigation

Draw a segment and label it AB. Draw an acute angle at A.

Copy A at point B on the same side of the segment.

Label the intersection of the two rays point C.

Use your compass to compare the lengths of AC and BC.
What do you notice?
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Converse of the Isosceles Triangle
Conjecture

If a triangle has two congruent angles, then _______________.

it is an isosceles triangle.
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Practice

Find the measure of T.
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Stations

Collaborative: Start your group project.

Independent: Get familiar with McGraw Hill

Direct: Practice.
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What’s wrong with this picture?

A
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Practice

Solve for r, s and t.
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Practice

The perimeter of ΔQRS is 344.

mQ=

QR=
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TODAY’S OBJECTIVES

Discover the relationship between the base angles of an
isosceles triangle.

Explain the sum of the measures of the angles of a triangle.

Write a paragraph proof.

Use problem solving skills.
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Exit Slip
For each question, show your work and explain your reasoning.
1.
Find x (above).
2.
mA=
3.
a=
4.
The perimeter of ΔABC=
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Honors Exit Slip
1.
Find x (above). Explain your
reasoning.
2.
mA=
3.
The perimeter of ΔABC=
4.
Use the diagram below to explain
why ΔPQR is isosceles.