Geometry Problem 1509: Congruence of Triangles in a Trapezoid and a Square, Measurement. Difficulty Level: High School.

In the following figure, ABCD is a trapezoid and CDEF is a square such that F is on AB. If BF measures 5 units and FA measures 2 units, calculate the measure of AD.

Geometry Problem 1509: Congruence of Triangles in a Trapezoid and a Square, Measurement. Difficulty Level: High School

Definitions and Suggestions

  • A triangle is a polygon that has three sides, three vertices, and three angles. Triangles are some of the most basic shapes in geometry and can be found in many different forms.
  • A trapezoid is a quadrilateral with at least one pair of parallel sides. Trapezoids are commonly encountered in geometry and in real-world applications, such as in architecture and engineering..
  • A square is a special type of rectangle where all four sides are of equal length and all four angles are right angles (90 degrees). Squares are commonly used in geometry and in real-world applications, such as in tiling, flooring, and building construction.
  • Two triangles are said to be congruent if all corresponding sides and angles of one triangle are equal to the corresponding sides and angles of the other triangle. There are several ways to prove that two triangles are congruent, including the Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), and Hypotenuse-Leg (HL) criteria.

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Discover Even More: See Also...

Problem 1510

Geometry Problem 1510: Congruence of Triangles, Perimeter, Measurement. Difficulty Level: High School

Problem 1508

Geometry Problem 1508: Understanding Triangle Geometry: Isosceles, Equilateral, Quadrilateral, Angular. Difficulty Level: High School

Problem 1507

Geometry Problem 1507: Understanding Triangle Geometry: Double Angles, Altitudes, and Measurements. Difficulty Level: High School

Problem 1506

Geometry Problem 1506: Parallel Rays, Angles. Difficulty Level: High School.

Problem 1505

Geometry Problem 1505: Three rays, Angles, Angle Bisector

Problem 1504

Geometry Problem 1504: Squares, Equilateral Triangle, Parallel, Angle

Thematic Poem: The Congruent Connection: A Poem of Trapezoids, Squares, and Geometry

The trapezoid stands tall and proud,
With parallel sides, it calls aloud.
Its height is long, and oh so high,
With angles meeting, it can't deny.

A square then comes to claim its place,
On the trapezoid's height, with great grace.
Their meeting point, they both have found,
And two right triangles now abound.

Their congruence is plain to see,
With sides and angles, all agreed.
The hypotenuses are the same,
And their measurements, all quite tame.

In geometry, this congruence is grand,
It helps us measure, plot, and plan.
We use it to build, create, and design,
In all aspects, of our earthly shrine.

So let us remember this tale so true,
Of a trapezoid and square, together anew.
With congruent triangles, all in their place,
Geometry's beauty, we can embrace.

If you're interested in finding more poems with a focus on geometry, you may enjoy this collection: More geometry thematic poems.

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