Geometry Semester Exam Dec 2024

Front

What is a congruence statement in geometry?

Back

Front

How do you find the height of a tree using proportions?

Back

To find the height of a tree using proportions, set up a ratio comparing the height of the tree to a known height and distance. For example, if a 6 ft person casts a 3 ft shadow and the tree casts a 12 ft shadow, the proportion is: \( \frac{height_{tree}}{12} = \frac{6}{3} \). Solving gives the height of the tree.

Front

What is the measure of angle w if it is corresponding to another angle measuring 55°?

Back

Angle w measures 55° because corresponding angles are equal when two parallel lines are cut by a transversal.

Front

Solve for x in the equation 2x + 4 = 16.

Back

x = 6.

Front

How do you find the x-coordinate of the midpoint of a line segment with endpoints (2, 4) and (0, 0)?

Back

The x-coordinate of the midpoint is found using the formula: \( x_{mid} = \frac{x_1 + x_2}{2} \). For the points (2, 4) and (0, 0), it is \( x_{mid} = \frac{2 + 0}{2} = 1 \).

Front

What is the definition of alternate interior angles?

Back

Alternate interior angles are pairs of angles that lie on opposite sides of a transversal and inside the two lines it intersects. They are equal when the lines are parallel.

Front

What is the Pythagorean theorem?

Back

Front

How do you calculate the area of a triangle?

Back

The area of a triangle can be calculated using the formula: \( Area = \frac{1}{2} \times base \times height \).

Front

What is the formula for the circumference of a circle?

Back

The circumference of a circle is calculated using the formula: \( C = 2\pi r \), where r is the radius.

Front

What is the definition of complementary angles?

Back

Complementary angles are two angles whose measures add up to 90 degrees.