Problem Solving in Geometry

Problem solving For Quadrilaterals:

Example 1:
70˚, 70˚, 40˚, what is the missing angle?

Proving your answer:

  • 1st you need to know what the sum of the interior angles of a quadrilateral equals.
  • You know that a Quadrilateral equals 360 degrees
  • So then you add 70+70+40 which equals 180
  • Now you subtract 360 – 180 = 180 and that would be your answer.
  • The missing angle is 180˚.
Example 2:
A quadrilateral has a 145˚ angle and a 16˚ angle. The remaining angles are congruent. What is the measure of both remaining angles?

Proving your answer:

Step 1: First you add 145+16= 176.
Step 2: So now you do 360-176= 184.
Step 3: Now you do 360-184= 176
Step 4: Now you do 176/2= 88
The missing angles are both 88˚.
Check your work!
Step 5: Now you do 145+16+88+88=360

Problem Solving for Triangles
Jack drew an Isosceles triangle. One of the angles is 90 degrees, and another is 45 degrees. What is the other angle? So, first we know that one angle is 90 degrees and another is 45 degrees. So, the first step is to add 90 plus 45 which equals 135. Next, you have to subtract 180 from 135 which is 45. So, the last angle must be……45! So than that means that it is a acute triangle.
Another problem that you might see is maybe this one…Zack has three different sized sticks. He puts them in the shape of a triangle. one of the sides is 38 inches and another is 105.What is the last side? OK! so we know that our magic number for triangles is 180.We know that one side is 38 inches and another is 105 inches. First we have to add 105 and 38 which is 143. Next you have to subtract 180 from 143 which is 37. So that means the last side must be…….37! So, that means that it is also a acute triangle.
Another you might see is one like this one…Kristine has some clay and she formed it into the shape of a triangle and all the sides are equal. One side is 60 inches. What are the other two sides? Okay dokey! We know that one side is 60 inches. So if all the sides are the same that must mean that the other two sides are also 60 inches! So now that means that it is also acute but remember not all problems they will turn out acute just these.
Here’s another...Samantha has a triangle like this one here. Classify this triangle by sides and angles! We know by looking at the picture that one side is 50 inches. So first we need to subtract 180 from 50 which is 130. Next you have to divide it by 2 which is 65 so the other 2 sides are 65 inches! So that means that it is also acute. Now, we have to classify it by sides. OK, it has two equal sides and one that is different than the other two sides. So that must means that it is a isosceles triangle.