#### Angles Geometry Problems

This angles quiz has problems with the following types of angles:

- Adjacent Angles - angles that share a common side and that have a common vertex

- Complementary Angles - angles which add together to make 90^{o}

- Supplementary Angles - angles that add together to make 180°

- Opposite Angles - when two lines intersect they create two pairs of opposite angles. Opposite angles are equal.

- Acute Angles - angles that are less than 90^{o}

- Right Angles - angles that are equal to 90^{o}

- Obtuse Angles - angles that are more than 90^{o} but less than 180^{o}

Angles in Plane Geometry

#### Problems with Bisectors, Medians and Altitudes

- The bisector of an angle is the line or line segment that divides the angle into two equal parts.

- The median of a triangle is a line segment that extends from one vertex of a triangle to the midpoint of the opposite side.

- An altitude is a segment from the vertex of a triangle to the opposite side that is perpendicular to that segment.

Bisectors, Medians and Altitudes Geometry Practice

#### Triangles Geometry Problems

This quiz has problems with right, scalene, obtuse, isosceles and equilateral triangles.

Some of the problems require knowledge of triangle similarity or congruence, Pythagorean Theorem, understanding of altitudes, bisectors and medians.

Triangles Geometry Practice

#### Quadrilaterals Geometry Problems

- Properties of different types of quadrilaterals: parallelogram, rhombus, trapezoid, rectangle, square

- Calculations of areas and perimeters of quadrilaterals

Quadrilaterals Geometry Practice

#### Circles Geometry Problems

- Properties of different types of quadrilaterals: parallelogram, rhombus, trapezoid, rectangle, square

- Calculations of areas, circumferences and arcs of circles

- Circles inscribed in triangles or quadrilaterals

- Circles circumscribed to triangles or quadrilaterals

Geometry Problems with Circles

#### Areas Geometry Problems

Problems that use the following areas formulas:

- Square: A = a^{2}, where *a* is the length of the side of the square.

- Rectangle: A = l×w, where *l* and *w* are the lengths of the rectangle's sides (length and width).

- Triangle: where *b* and *h* are the base and height

- Circle: A = πr^{2} where *r* is the radius.

- Trapezoid: where *a* and *b* are the lengths of the parallel sides and h the height of the trapezoid.

Geometry Practice with Areas of Geometric Figures

#### Pythagorean Theorem Geometry Problems

The Pythagorean Theorem states that for a right triangle with legs *a* and *b* and hypotenuse *c*,

c^{2} = a^{2} + b^{2}

The Cosine Law is a generalization of the Pythagorean Theorem. For a triangle with sides *a*, *b*, and *c* and angle *C* opposite the side *c*,

Pythagorean Theorem Geometry Quiz

#### Equations in Geometry Problems

- Equations of lines, slope, x-intercept and y-intercept

- Points of intersection of lines, parallel lines, perpendicular line in the Cartesian coordinate system

- Equations of circles, coordinates of the center of a circle

- Points of intersection between lines and circles, lines tangent to circles

Equations of Geometric Figures

#### Problems with Trigonometric Identities

- Problems with the unit circle, definition of sine, cosine, and tangent

- Problems with trigonometric equations and identities

- Trigonometry with right triangles

Trigonometric Identities Quiz

#### Modeling Geometry Problems

Modeling with geometry problems test students in the following critical areas:

- application of geometric concepts in modeling situations

- use of geometric shapes, their measures, and their properties to describe objects

- application of concepts of density based on area and volume in modeling situations

Modeling Geometry Problems