COURSE TITLE:  Algebra I

AUTHOR:  Helaine Clegg

TOPIC:  Solving Proportions Using Similar Triangles

PERFORMANCE OBJECTIVE:  You will find missing parts of similar triangles by using ratio and proportion.

MATH STANDARD #10.G.4:  Apply congruence and similarity correspondences and properties of the figures to find missing parts of geometric figures, and provide logical justification.

ACTIVITY#1:  Click here for a review of proportions.

    The picture of the two pyramids below is an example of similar triangles.  Similar triangles are triangles that have the shape.  Their corresponding angles have the same measure and their corresponding sides are in proportion.

    There are three similar triangles in the picture of the molecule below.  Can you find them?

    The two triangles below are similar triangles.  The corresponding angles have the same measure and the corresponding sides are in proportion.

    Triangle ABC is similar to Triangle DEF.  Therefore, angle A corresponds to angle D, angle B corresponds to angle E, and angle C corresponds to angle F.  Notice the single slash mark through angles D and A.  That slash mark means that those angles correspond.  They have the same measure.  Notice the two slash marks through angles E and B.  That slash mark means that those angles correspond.   They have the same measure.  Notice the sqaure on angles F and C.  Those two angles are corresponding angles.  They have the same measure.

    The sides of the triangle also correspond.  Side DE corresponds to side AB.  Side DF corresponds to side AC.  Side FE corresponds to side CB. These sides do not have the same measure.  The sides are in proportion.

DE/AB = DF/AC = FE/CB

To find side a, write a proportion using the corresponding sides.

5/10 = 3/a (Remember to solve proportions, cross multiply, then solve for the variable)

5a = 30, so a = 6.  Side a measures 6.

To find side b, write a proportion using the corresponding sides.

5/10 = 4/b (Remember to solve proportions, cross multiply, then solve for the variable)

5b = 40, so b = 8.  Side b measures 8.

Now you try to identify the corresponding sides and angles of the triangles below.

1.) 

Angle A corresponds to angle _______               

Angle B corresponds to angle ______

Angle c corresponds to angle _______

Side d corresponds to side ____

Side b corresponds to side _____

Side f corresponds to side _____

2.)  List the corrersponding sides and angles of the triangles below.

Side _____ corresponds to side ______

Side ______ corresponds to side ______

Side  _____ corresponds to side ______

Angle _____ corresponds to angle _____

Angle _____ corresponds to angle ______

Angle _____ corresponds to angle ______

Now it's your turn to try to find the missing sides of the similar triangles below.

3.)  Triangle WXY is similar to Triangle WAT

Find WX ______  Find YT_______  Find XA ______  Find AT ________

4.)  Triangle ABC is similar to Triangle DEC

Find CB _____  Find AD ______  Find EB _______ Find DE _______

5.)  Triangle ABC is similar to Triangle CBD is similar to Triangle ACD.   Angle C is a right angle.  Line CD is perpendicular to Line AB.  Angle A measures 60 degrees.

Find measure of angle 1 ______  angle 2 _______ angle 3 ______ angle 4 _______

For each of the similar triangles below, find x.

6.)  x = _______

7.)  x = ________

8.)  x = ________

9.)  x = __________