Constructing Triangles

Unit 4C-Triangle Geometry

• LT5: I can construct triangles from given angles.

• LT6: I can construct triangles from given sides.

Drawing TrianglesThere are 4 different ways you can draw triangles…

1.) SAS (Side-Angle-Side)2.) ASA (Angle-Side-Angle)3.) AAA (Angle-Angle-Angle)4.) SSS (Side-Side-Side)

SAS (Side-Angle-Side)A triangle can be constructed if we are given 2 sides and an angle.

For these triangles, both a protractor AND a ruler are essential.

The following video clip will offer an introduction on how to draw SAS triangles.

PAY ATTENTION!!!!!!!!!!

If the two sides include (join) the angle, the angle is called an “included angle”

SAS (Side-Angle-Side)

http://www.youtube.com/watch?v=gwKaluvCLrU

Now we will practice with a few examples.

Clear your area of everything EXCEPT a pencil, blank paper, ruler, protractor, and scissors.

Create the following triangles on your blank paper based on SAS given.

Examples

1.) AB=4 cm, Angle A =30˚, AC=5 cm

2.) BC=3 cm, Angle B=80˚, BA=6 cm

Now cut your triangles out and place them on your neighbor’s to see if they are the same fit!

**For BOTH examples you are creating Triangle ABC**

ASA (Angle-Side-Angle)A triangle can be constructed if we are given 2 angles and a side.

For these triangles, both a protractor AND a ruler are essential.

The following video clip will offer an introduction on how to draw ASA triangles.

PAY ATTENTION!!!!!!!!!!

If the two angles include (share) the side, the side is called an “included side”

ASA (Angle-Side-Angle)

Now we will practice with a few examples.

Make sure you have cleared your area of everything EXCEPT a pencil, blank paper, ruler, protractor, and scissors.

Create the following triangles on your blank paper based on ASA given.

http://www.youtube.com/watch?v=Hawuf6Sh070

Examples

1.) Angle A=40˚, AC=5 cm, Angle C=30˚

2.) Angle A=20˚, AC=6.5 cm, Angle C=90˚

Now cut your triangles out and place them on your neighbor’s to see if they are the same fit!

**For BOTH examples you are creating Triangle ABC**

AAA (Angle-Angle-Angle)A triangle can be constructed if we are given 3 angle measures.

Step 1: Sketch a triangle as a model for what to create.

Step 2: Fill in the given information (angle measures) where you would like for them to go when you draw your “real” model

Step 3: Now start with one line segment (base of the triangle) and create 2 of the required angles from the base (one on left and one on right)

Step 4: Check the third angle once all line segments are connected to ensure it meets the requirements given for the third angle.

**Remember to make sure a triangle can be formed before you start**

Examples

1.) Angle A=40˚, Angle B=60˚, Angle C=80˚

2.) Angle A=25˚, Angle B=120˚, Angle C=35˚

Now cut your triangles out and place them on your neighbor’s to see if they are the same fit!

SSS (Side-Side-Side)A triangle can be constructed if we are given 3 side measures.

Step 1: Sketch a triangle as a model for what to create.

Step 2: Fill in the given information (side measures) where you would like for them to go when you draw your “real” model

Step 3: Now start with one line segment (base of the triangle) and draw it the length of the measure given

Step 4: You will have to build up the other 2 sides of the triangle using your ruler and meeting the measures given. You will most likely have to use trial and error to get the triangle formed correctly.

**Remember to make sure a triangle can be made before you start**

Examples

1.) AB=4 cm, AC=6 cm, BC=7 cm

2.) AB=3 cm, AC=5 cm, BC=4 cm

Now cut your triangles out and place them on your neighbor’s to see if they are the same fit!

Homework

• You are to complete (draw) the following 4 triangles on your own piece of paper to turn in tomorrow when you enter the classroom.

**You are creating Triangle ABC in all 4 problems• 1.) AB=3cm, Angle A=90°, AC=4cm• 2.) Angle A=65°, AB=12cm, Angle B=65°• 3.) Angle A=35°, Angle B=120°, Angle C=25°• 4.) AB=3.5cm, BC=5.5cm, AC=7cm