Download Drawing Triangles

Drawing Triangles
We know that triangles have six measurable parts: three sides and three angles. But we also know that some recipes for
drawing triangles don’t specify all six parts; nevertheless, if two people follow the recipe, they are guaranteed to draw
congruent triangles. Today’s activity follows up on this observation by asking you to draw triangles using only as much
information as is absolutely necessary to guarantee that there is only one possible triangle with those measurements. Our
goal is to determine how many and what kinds of measurement are necessary.
Instructions:
1. For each triangle, read one measurement at a time.
2. Use the right side of the page to draw your triangle or assemble it from spaghetti as you go along. TAPE or DRAW
your triangle in the space provided.
Spaghetti Constructions
It may be easier to construct your triangle using pieces of spaghetti instead of ruler,
compass, and protractor. It’s really a matter of personal preference.
 Break off pieces of spaghetti corresponding to the lengths given.
 Arrange long or unbroken strands for angles if you don’t know the lengths of
both enclosing sides. That way you can break the strand later when you
determine the correct length.
 Tape down pieces of spaghetti as you go along.
3. AS SOON AS you have enough information to finish drawing the triangle (without needing more information), draw
a line across the page to indicate where you stopped.
4. Then check that the triangle you drew satisfies the rest of the given information.
Triangle #1
1. AB = 8 cm.
2. BC = 6 cm.
3. AC = 10 cm.
4. m ACB = 53°.
5. m ABC = 90°.
6. m BAC = 37°.
Triangle #2
1. AB = 8 cm
2. AC = 7 cm
3. m BAC = 40°
4. m ACB = 80°
5. m ABC = 60°
6. BC = 5.2 cm
Triangle #3
1. m ABC = 30°
2. m ACB = 40°
3. m CAB = 110°
4. BC = 6.5 cm
5. AB = 4.8 cm
6. AC = 3.4 cm
 Was item #3 really helpful for this triangle? Why or why not?
Triangle #4
1. AB = 10 cm
2. AC = 8 cm
3. m ABC = 35°
4. m BAC = 99°
5. m ACB = 46°
6. BC = 13.8 cm
 Try to draw a different triangle satisfying items 1-3. If you need a hint, see your teacher.
Reflect:
 Is a pair of sides, and the angle between those sides, enough to guarantee a unique triangle?
 What other sets of information are enough to guarantee a unique triangle?
 What appears to be the minimum number of measurements you need to construct a triangle?
 Would you ever need all 6?
 Say you have the minimum number of measurements, and that they are a combination of sides and angles. Does it
matter which sides and angles you are given, or would any combination create a unique triangle?