Type of Class:
             Standard High School Geometry

Related VA SOL: G.5

Time Frame:
          Ninety-minute block period

Objectives:

• Students will know how to identify if triangles are congruent.

• Students will know how to identify if triangles are similar.

Materials:

• Protractor

• Chalkboard

• Rulers (if available)

Procedures:

1)      Investigating congruence in triangles

a)      Two triangles are said to be congruent if they have the same shape and size

i)        Congruent triangles have congruent corresponding parts.  The matching angles and sides of congruent triangles are called corresponding parts.  Matching vertices are corresponding vertices.  When naming congruent triangles, always list corresponding vertices in the same order.

ii)       For example:

b)      At their desks, have students draw 2 pairs of congruent triangles with rulers and protractors.  Make sure that each of the 2 pairs of triangles the students draw are different in side length and in angle measurement.  Encourage students to rotate triangles so the sides are facing different directions.

i)        Provide examples on an overhead, as below:

ii)       Once they are all complete, call a couple of students to the board to share their constructions.

2)      Investigating similarity in triangles

a)      Two triangles are said to be similar (denoted by {~}) if:

• Corresponding angles are congruent

• Corresponding sides are proportional

b)      The ratio of the lengths of corresponding sides is the similarity ratio.

 c)      Example to be done by teacher using the diagram below:

i)        How to find the similarity ratio:

Answer: Since segment FR and segment DA are corresponding sides of similar triangles, the similarity ratio is.

ii)       How to find m

Answer: R corresponds to A, so mR = mA

The mA = , so mR = .

iii)     How to solve for the length of segment RI

Answer:

d)      Have the students form groups of two or three.  Using the triangles above, find:

i)        Segment DY, measure of angle D

ii)       Perimeter of

• What is the ratio of the two perimeters?

e)      Compare answer of b(iii) to c(ii-1) to the similarity ratio.  Make a conjecture about the ratio of the perimeters of similar triangles.

f)        In the same groups, have the students test their conjecture by creating two distinct pairs of similar triangles using a protractor and ruler.

Assessment: In groups, have students create 3 sets of similar triangles with necessary measurements, as above.  The groups will then exchange work and solve for the desired information.

Suggestions/Comments: Picking the students groups instead of letting them choose their own will cut down on wasted time, as will passing out rulers and protractors before the lesson begins.