# Tag Archives: triangle

## Non-Congruent Triangles

Among the triangles of the previous problem (repeated below), how many distinct (non-congruent) triangles exist? Previous Problem: How many distinct triangles can be constructed by choosing three vertices from among the corners of a unit cube? Source: NCTM Mathematics Teacher, … Continue reading

## Distinct Triangles

How many distinct triangles can be constructed by choosing three vertices from among the corners of a unit cube? Source: NCTM Mathematics Teacher, February 2008 Solution We construct four triangles from three corners of a face for a total of … Continue reading

## Sum of Six Angles

Find the value in degrees of the sum of the six angles indicated in the diagram. Source: NCTM Mathematics Teacher, February 2008 Solution The three triangles contain nine angles, three of which form a straight angle. Hence, the sum of … Continue reading

## Area of Trapezoid

In a trapezoid with parallel to , the diagonals intersect at point . The area of triangle is , and the area of triangle is . Find the area of the trapezoid. Source: NCTM Mathematics Teacher, August 2006 Solution Draw … Continue reading

## Making Triangles

You have six sticks of lengths , and cm. Find the number of noncongruent triangles that can be formed using three of these sticks as sides. Source: NCTM Mathematics Teacher, August 2006 Solution Three sticks make a triangle. There are … Continue reading

## Area of Triangle

Without using Heron’s formula, find the area of the triangle. Source: NCTM Mathematics Teacher, January 2006 SOLUTION Applying the Law of Cosines Area of triangle Answer: square units Alternative solution 1 Most textbooks state the Law of Sines as We have … Continue reading

## Sticks in a Bag

Each stick in a certain bag has integral length. If any three sticks are selected from the bag, they will not form a triangle. The longest stick in the bag has length . What is the maximum number of sticks … Continue reading

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## Altitude

In triangle , and . If is a point on such that is perpendicular to , what is ? Source: NCTM Mathematics Teacher, November 2006 SOLUTION Area of triangle by Heron’s formula Area of triangle Area of triangle using base … Continue reading

## Triangle in Three Dimensions

Calculate the area of triangle with the following vertices: , and . Source: NCTM Mathematics Teacher, February 2006 SOLUTION Apply the distance formula in three dimensions Apply Heron’s formula for the area of a triangle with side lengths area = … Continue reading