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

Given the figure where triangles ABC, ECD, and DFG are congruent, the perimeter of triangle ABC is 124 units, EF measures 24 units, and AD measures 14 units, find the length of AB in units.

Geometry Problem 1510: Congruence of Triangles, Perimeter, 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.
  • The perimeter of a triangle is the sum of the lengths of its three sides.
  • 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 1511

Geometry Problem 1511: Finding the Altitude of an Isosceles Triangle Using Distances from a Point on the Extension of the Base. Difficulty Level: High School

Problem 1509

Geometry Problem 1509: Congruence of Triangles in a Trapezoid and a Square, 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

 

Thematic Poem: Congruent Triangles: Discovering Perimeter and Beauty in Three Equal Shapes

Three triangles, congruent they are,
Equal in size, near or far,
Their perimeters, oh so grand,
Are equal, in every land.

The sides of each triangle match,
Equal in length, without a scratch,
Their angles too, a perfect match,
Three congruent triangles, what a catch!

To find the perimeter of this trio,
We add up the sides, oh so easy, though,
Three times the sum, we need to know,
And the answer will beautifully show.

Congruent triangles, a wonder to see,
In every shape, in every degree,
And through their congruence, we can see,
The beauty of math, in all its glory.

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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