Formulas: Geometric Concepts [TEKS Tools Grade 8]

This post specifically looks at how formulas can be used solve problems involving similar shapes and the Pythagorean Theorem. Read more about TEKS Tools and their rationale here.

Formulas

Formulas account for around 38% of each 8th grade STAAR test. These formulas are applied to solve problems related to volume, surface area, triangles, similar shapes, linear relationships, and finances.

The main function of a formula is to understand the relationship between quantities. In fourth grade, students were first introduced to the formulas for area and perimeter of squares and rectangles. In fifth grade, they were introduced to the formula for volume of a rectangular prism. In sixth grade, the formulas for area of a triangle, parallelogram, and trapezoid are explored. In 7th grade, students are introduced to surface area and to circle geometry, exploring π (pi), circumference, and area. Now in 8th grade, students stabilize their previous learning about linear relationships, surface area, volume (including composite shapes), and finances while beginning to explore geometric concepts such as the Pythagorean Theorem.

Similar Shapes

Two right triangles are similar when a line can be drawn that includes both hypotenuses.

8.4A - use similar right triangles to develop an understanding that slope, m, given as the rate comparing the change in y- values to the change in x- values, (y2 - y1 ) / (x2 - x1 ), is the same for any two points (x1 , y1 ) and (x2 , y2 ) on the same line

2023-5: two similar right triangles were given, students had to represent the slope of the hypotenuse as a proportion

2024-36: a right triangle and a line were given, students had to identify the vertex of a similar triangle

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Pythagorean THeorem

8.6C - use models and diagrams to explain the Pythagorean theorem

2023-4: a diagram with three squares connected to a right triangle was given, students had to find the correct description of the model

2025-27: a diagram with three squares connected to a right triangle was given, along with the area of two squares, and students had to find the side length of one of the squares

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8.7C - solve problems involving the volume of cylinders, cones, and spheres

2023-23: two sides of a parallelogram were given, students had to use the Pythagorean theorem to prove that the parallelogram was a rectangle

2024-19: two sides of a right triangle were given, students had to find the length of the hypotenuse

2025-19: a leg and the hypotenuse of a right triangle were given, students had to find the length of the other leg

2025-23: internal and external side lengths of a kite were given, students had to use the Pythagorean theorem to find missing side lengths

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8.7D - determine the distance between two points on a coordinate plane using the Pythagorean Theorem

2024-22: two points on a coordinate plane were given, students had to use the Pythagorean theorem to find the length

2025-15: a line segment on the coordinate plane was given, students had to use the Pythagorean theorem to find the length