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Proving Triangle Theorems

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Aligned To Common Core Standard:

Trigonometry - HSG-SRT.B.4

How to Prove Triangle Theorems - 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. When we type a triangle based on their sides, then we look at their lengths. If the lengths of all sides are equal, then the triangle is equilateral. If two of its sides are equal, then it is an isosceles triangle and if all sides are unequal, then the triangle is scalene. When we classify the triangle based on angles, then we measure the size of the angle. If there is a side with an angle is 90°, then the triangle is called the right-angled triangle. If all the angles are less than 90°, then the triangle is acute. While if one of the angles has a size of more than 90°, then the triangle is an obtuse triangle. 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°. These worksheets and lessons show students the steps to take when writing triangle proofs with well documented theorems.

Printable Worksheets And Lessons

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 = ____.