### Constructing Triangles

```Constructing Triangles
Unit 4C-Triangle Geometry
• LT5: I can construct triangles from given
angles.
• LT6: I can construct triangles from given sides.
Drawing Triangles
There are 4 different ways you
can draw triangles…
1.)
2.)
3.)
4.)
SAS (Side-Angle-Side)
ASA (Angle-Side-Angle)
AAA (Angle-Angle-Angle)
SSS (Side-Side-Side)
SAS (Side-Angle-Side)
A triangle can be constructed if we are given 2 sides and
an angle.
If the two sides include (join) the angle, the angle is
called an “included 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!!!!!!!!!!
SAS (Side-Angle-Side)
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
**For BOTH examples you are creating Triangle ABC**
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!
ASA (Angle-Side-Angle)
A triangle can be constructed if we are given 2 angles and
a side.
If the two angles include (share) the side, the side is
called an “included 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!!!!!!!!!!
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.
Examples
**For BOTH examples you are creating Triangle ABC**
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!
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
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
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
```