Geometry Fall Final Review

Front

What is the point of concurrency that is the intersection of a triangle's three medians?

Back

Centroid

Front

If \( \angle 3 \) and \( \angle 4 \) are vertical angles, and \( m\angle 3 = 4x - 5 \) and \( m\angle 4 = 7x - 26 \), what is the measure of \( \angle 3 \)?

Back

x = 23

Front

Given that lines p and q are parallel, what is the value of x if the corresponding angles are equal?

Back

x = 11

Front

Which of the following statements is false regarding angles formed by two parallel lines cut by a transversal?

Back

\( \angle 1 \) and \( \angle 8 \) are alternate interior angles.

Front

What is the inverse of the statement: 'If you exercise regularly, then you will be healthy'?

Back

If you do not exercise regularly, then you will not be healthy.

Front

Define the term 'vertical angles'.

Back

Vertical angles are the angles opposite each other when two lines intersect. They are always equal.

Front

What is the definition of 'alternate interior angles'?

Back

Alternate interior angles are pairs of angles that lie on opposite sides of the transversal and inside the two lines.

Front

What is the definition of 'corresponding angles'?

Back

Corresponding angles are pairs of angles that are in the same position on two parallel lines in relation to a transversal.

Front

What is the formula for finding the centroid of a triangle given its vertices?

Back

The centroid (G) can be found using the formula: \( G \left( \frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3} \right) \) where \( (x_1, y_1), (x_2, y_2), (x_3, y_3) \) are the vertices.

Front

What is the relationship between the angles formed by a transversal intersecting two parallel lines?

Back

The angles formed have specific relationships: corresponding angles are equal, alternate interior angles are equal, and consecutive interior angles are supplementary.