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