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Proving Triangle Theorems Worksheets

The pillar of writing geometric proofs to explain things is that well know figure the triangle. There are endless applications that can be applied to it to be used as a tool to help you understand more about your surroundings. When you are in doubt look for a triangle to save the day. This is all because a small number of qualities that have been recognized over time by mathematicians. These worksheets and lessons show students the steps to take when writing triangle proofs with well documented theorems.

Aligned Standard: High School Geometry - HSG-SRT.B.4

  • Answer Keys - These are for all the unlocked materials above.

Homework Sheets

These are great starter proofs for you.

  • Homework 1 - The sum of the measures of the angles of a triangle is 180 degrees. This helps us through the rest of the problem.
  • Homework 2 - You can set it up as:
  • Homework 3 - According to ASA Theorem, if two angles are equal then the other two sides are also equal.

Practice Worksheets

Time to remember all those crazy theorems we have been going over.

  • Practice 1 - Find the length of PR by using the side splitter theorem. PQ = 8 PR = ? QS = 16 RT = 20
  • Practice 2 - The triangle is isosceles triangle. Use that knowledge to calculate the value of x in the diagram.
  • Practice 3 - Two of the three angles of the triangle ABC are 120 degrees and 40 degrees. Calculate the measure of the third angle.

Math Skill Quizzes

See what you think of thoughts of reflection and visualization here.

  • Quiz 1 - In triangle DEF, m
  • Quiz 2 - Are there any line reflections in this image?
  • Quiz 3 - If P = 45 degrees, then Q = ____.

How Classify to Triangles

Female Ranger

A triangle is a shape with only three sides so that they can be classified by their sides or by their angles. All the theorems constructed for the triangles are overviewed in this section independently. Before we begin breaking these things down, we need to know how triangles are classified. They can be classified, like everything else that comes with these figures, by either the length of their sides or the three interior angles.

When we classify a triangle based on the length of their sides, then we look at their lengths across the entire figure. If the lengths of all sides are equal, then it is an equilateral. If two of its sides are equal, then it is an isosceles and if all sides are unequal, then it is classified as scalene.

When we classify the triangle based on angles, then we measure the angle. If there is a measure with an angle is 90°, then the triangle is called the right triangle. If all the angles are less than 90°, then it is referred to as being acute. While if one of the angles has a value of more than 90°, then it is called obtuse.

The classification of these triangles eventually leads to solving all the theorems constructed for different sides of the triangle. For instance, the Triangle Angle Sum Theorem, where the sum of all the angles is 180°.

What Are the Important Triangle Theorems?

There are three foundational theorems in the world of triangles that opens up a whole bunch of new possibilities to the everyday real world. These simple things allow us to understand a great deal about coordinate plane and physical situation.

Foundational Theorem 1 - ∠A + ∠B + ∠C = 180°,

The sum of all the interior angles of a triangle are equal to 180 degrees. This helps us find any missing angle, as long as we know the measures of the two angles.

Foundational Theorem 2 – Base angles of isosceles triangles are congruent.

If you remember, an isosceles triangle has two sides that are the same length and as a result they form congruent base angles. If you know the classification of the triangles you are working with, you can instant learn the measures of a missing side or angle when we know the measures of another.

Foundational Theorem 3 – If we extend our the line of side of a triangle we will find that the exterior angle that we have create is equal to the sum of the corresponding interior angles. Since we know that we can determine the measures of an interior angle because it is a supplementary angle to exterior angle, it empowers us to quickly learn the measure of other angles quickly.

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