# Tag Archives: geometry

## 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

## Measure of Angle Z

Find the measure of the angle in the diagram here, given that the two horizontal segments are parallel. Source: NCTM Mathematics Teacher, February 2008 Solution Complete a seven-sided concave polygon by drawing a perpendicular line to the two parallel lines … Continue reading

## Four Congruent Rectangles

Four congruent rectangles are arranged as shown in the figure to form a large rectangle. The area of the large rectangle is . What is the area of a square that has the same perimeter as the large rectangle? Source: … 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

## Equilateral Triangle and Regular Hexagon

What is the ratio of the area of an equilateral triangle to that of a regular hexagon inscribed in the same circle? Source: NCTM Mathematics Teacher, February 2008 Solution The hexagon is made up of six congruent isosceles triangles three … 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

## Tangent Circles

Consider the circles that have radii and are tangent to the line at the point . Find the sum of the coordinates of the centers of the circles. Source: NCTM Mathematics Teacher, August 2006 Solution For the two circles to … Continue reading

## Round Table

A round table can be made square by dropping the four leaves. If a side of a square table measures inches, to the nearest hundredth of a square inch, how much smaller is the area of the table when the … Continue reading

## Largest Equilateral Triangle in a Square

How long is the side of the largest equilateral triangle that can be inscribed in a square with side length ? Source: NCTM Mathematics Teacher, August 2006 Solution A first guess is an equilateral triangle of side length . Could … Continue reading