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Group: Greg Qualiana, Brittany Ponivas, Matthew Garozzo
Title: Isosceles Triangles
Date: Tuesday October 16, 2007
Grade Level: Math A, Grade 10
Materials: Handouts, writing utensil, notes, paper
Lesson Overview: Students will work with properties of Isosceles triangles and
solve algebraic equations to develop an understanding of angles.
Lesson Objectives: By the end of the lesson students will be able to evaluate
equations to determine the measures of angles. Students will be able to propose
a plan of their understanding of Isosceles triangles by filling in blank angles in a
diagram or propose an answer by evaluating equations.
NYS Standards:
Anticipatory set: (5 minutes) Start off by reviewing Monday’s material. Write
three triangles on the board, one isosceles, one equilateral and the third scalene.
Have the students give some facts about each, whatever they remember, to
bring up previous knowledge.
Developmental Activity: (25 minutes) First draw a blank diagram of the triangle
and the italicized words below on the board. Have the students get their
notebooks out to take notes. Have the students go over every term in the box
and write the definitions next to the terms on the board. They should know some
facts, if not all, by now. After you go over the term ask the students if they can
come up to the board and fill in the example. Have them label each angle.

An isosceles triangle has two congruent sides and two congruent angles.
The congruent sides are called legs and a third side called the base.

The vertex angle is the angle included by the congruent legs.

The other two angles are called base angles.

The base angles are congruent.
Then go over the term exterior angle. Draw the diagram on the board
along with the definition and examples. An exterior (or external) angle is the
angle between one side of a triangle and the extension of an adjacent side. For
example <ABC, or <ECD. You don’t really need to go over this in detail because
they should already have previous knowledge of this. Also mention the
interesting fact: An exterior angle is congruent to the sum of the non-adjacent
angles in a triangle. For example, <ABC = <BCD+<CDB.
Next, hand out the activity for the day. After handing out the activity, go
over the first example on the board. Ask the students a few questions. “Who can
tell me which angles are congruent?” or “Tell me some characteristics of this
triangle.” Some expected responses should be anything from the terms in the
box above. This will emphasize the terms they learned earlier. Have the
students work on the worksheet individually. This can be an assessment so walk
around and see if anyone is struggling.
Closure: (5 minutes) Make sure everything is erased from the board and have
the students “Sum up the Day”, which is basically wrapping everything up by
going over the definitions and facts. Make a list on the board and tell them to
write it down.
Homework: (5 minutes) This will be the “Ticket out the door”. Hand it out and
say Good Luck!
Activity Of The Day, Yay!
Name:
Directions: Complete the worksheet solve for x and find the measurements of
the angles given.
1.
Line AB=AC
m BCA = 5x – 46 =_____
m BAC = 2x + 8=_____
2.
Line AC =AB
m DCE = 72=_____
m CBA = x=_____
3.
m
m
m
m
DBE = m DEB
ABD = 123
DBE = x
BDE=_____
4.
Line DC= BD
m DCE = 3x + 16=_____
m CBD = x =______
m DCB=_____
5.
Line AB=AC
m DCE = 4x + 38=_____
m CBA = 3x + 31=_____
m CAB=_____
6.
m CBD= m BDC
m CBD = 40
m DCE = x=_____
Ticket Out The Door
Example 1: An isosceles triangle has one angle of 96º. What are the sizes of the
other two angles?
Example 2: A right triangle has one other angle that is 45º. Besides being right
triangle what type of triangle is this? Explain how you know.
Answers for Teachers
Activity for the day
1.
2.
3.
4.
5.
6.
Line AB = AC, x=27.25, m<BCA=90.25, m<BAC=62.5
AC=AB, m<CBA=72
<DBE=57
x=41, <DCE=139, <CBD=41, <DCB=41
x=-7, <DCE=10, <CBA=10
<DCE=100
Ticket Out The Door
1. 42
2. 45, Isosceles Triangle