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# Category Archives: Geometry

## Translation Coordinates and Graph of Translated Image example question

Find the coordinates and the translated graph of A(-2, 3), B(4, -5), and C(0, 3) by following the rule of translation:

(x, y) → (x – 5, y + 6).

Solution to this Translation Geometry practice problem is given in the video below!

## Finding Coordinate RULE of Translation given Graph of Translated Image example problem

Find the coordinate rule for the translation shown in the graph below. Solution to this Translation Geometry practice problem is given in the video below!

## Dilation Formulas and Graph with Origin the Center of Dilation example question

Graph the triangle with vertices A(-2, 4), B(1, -4), C(-3, -2) and its image after dilation by scale factor k = -3. The center of dilation is the origin.

Solution to this Dilation Geometry practice problem is given in the video below!

## Dilation Formulas and Graph with Center of Dilation NOT the Origin example problem

Graph the triangle with vertices A(-2, 4), B(1, -4), C(-3, -2) and its image after dilation by scale factor k = 2. The center of dilation is the point (4, 5).

Solution to this Dilation Geometry practice problem is given in the video below!

## Reflection Formulas example question

Draw the image of the polygon with coordinates A(-2, 3), B(0, 2), C(3, -4), D(4, 0) by reflecting it

a) through the y-axis

b) through the x-axis

c) through the origin

d) through the line y = x

Solution to this Reflection Geometry practice problem is given in the video below!

## Rotation Formulas example question

a) Draw the image of the triangle with coordinates A(-6, -6), B(-6, 3), C(-2, 3) by rotating it 90 degrees clockwise

b) Draw the image of the quadrilateral with coordinates A(-3, -3), B(-1, 0), C(3, 0), D(5, -3) by rotating it 90 degrees counterclockwise

c) Draw the image of the triangle with coordinates A(-3, 2), B(1, 5), C(0, 0) by rotating it 90 degrees clockwise

d) Draw the image of the triangle with coordinates A(1, -3), B(3, 3), C(6, -3) by rotating it 180 degrees clockwise or counterclockwise

e) Draw the image of the quadrilateral with coordinates A(-5, -2), B(-4, 5), C(2, 5), D(2, 0) by rotating it 90 degrees clockwise

Solution to this Rotation Geometry practice problem is given in the video below!

## Solving for X and Y in Angles example question

Find the values of x and y using the figure below. Use these values to find the following:

a) b) c) d) Solution to this value of x and y in Angles Geometry practice problem is provided in the video below!

## Angle Theorems Parallel Lines and Transversals example question

The following figure shows two parallel lines l and m and a transversal. Use this figure to answer the following questions:

a) b) c) d) e) f) g) Solution to this Angles Parallel Lines Transversal Geometry practice problem is provided in the video below!

## Angle Theorems Parallel Lines and Transversals example problem #2

Use the following figure to find the values of x and y Solution to this Angles Parallel Lines Transversal Geometry practice problem is provided in the video below!

## Angle Theorems Parallel Lines and Transversals example #3

Use the figure below to solve for the values of x and y Solution to this Angles Parallel Lines Transversal Geometry practice problem is provided in the video below!

## Angle Theorems Parallel Lines and Transversals example question #4

Use the given figure below to find the values of x and y Solution to this Angles Parallel Lines Transversal Geometry practice problem is provided in the video below!

## Angle Theorems Parallel Lines and Transversals example problem #5

The figure below shows a polygon with some interior angle measures provided. Find the values of x and y

Solution to this Angles Parallel Lines Transversal Geometry practice problem is provided in the video below!

## World’s HARDEST Easy Geometry problem example question

The following triangle, , shows angle measures in the base angles A and C, as well as line segments , and . Find the measure of angle AED, that is, .

Note: Do not use Trigonometry or Calculus to solve this problem Solution to this World’s Hardest Easy Geometry practice problem is provided in the video below!

## Centroid Circumcenter Incenter Orthocenter properties example question

In the following video you will learn how to find the coordinates of the Orthocenter located outside the triangle in the standard xy-plane (also known as coordinate plane or Cartesian plane). In acute and right triangles, the Orthocenter does not fall outside of the triangle. However,  when the triangle in question is obtuse, that is, when one of its interior angles measures more than 90 degrees – the Orthocenter will be located outside the triangle. This is when you will need to understand the technique used to find its coordinates.

Solution to this Orthocenter in Obtuse Triangle Geometry practice problem is provided in the video below!

## Centroid Circumcenter Incenter Orthocenter properties example question

In this video you will learn the basic properties of triangles containing Centroid, Orthocenter, Circumcenter, and Incenter. Then you can apply these properties when solving many algebraic problems dealing with these triangle shape combinations.

Solution to this Centroid Circumcenter Incenter Orthocenter Geometry practice problem is provided in the video below!

## Two Column Geometry Proof Intersecting Lines example problem Given: GA = RA, AH = AT

Prove: GT is congruent to RH

Solution to this Two Column Geometric Proof practice problem is given in the video below!

## Two Column Geometry Proof Trapezoid example Given: AD = 8, BC = 8, and BC is congruent to CD

Prove: AD is congruent to CD

Solution to this Two Column Geometric Proof practice problem is given in the video below!

## Two Column Geometry Proof Circle example question Given: is a diameter Solution to this Two Column Geometric Proof practice problem is given in the video below!

## Two Column Geometry Proof Triangle example problem Given: Prove: Solution to this Two Column Geometric Proof practice problem is given in the video below!

## Two Column Geometry Proof Triangle example #2 Given: with the bisector of  Prove: BFDE is a rhombus

Solution to this Two Column Geometric Proof practice problem is given in the video below!

## Two Column Geometry Proof Circle example question #2 Given: Circle with center O and diameter  Prove: Solution to this Two Column Geometric Proof practice problem is given in the video below!

## Two Column Geometry Proof Kite example problem Given: Kite ABCD with E, F, G, H are midpoints of Prove: EFGH is a rectangle

Solution to this Two Column Geometric Proof practice problem is given in the video below!

## Two Column Geometry Proof Triangle example #3 Given: bisects  is a perpendicular bisector of Prove: Solution to this Two Column Geometric Proof practice problem is given in the video below!

## Two Column Geometry Proof Triangle example question #4 Given: is isosceles and Prove: Solution to this Two Column Geometric Proof practice problem is given in the video below!

## Two Column Geometry Proof Parallel Lines Transversal Triangle example problem Given:  bisects  bisects Prove: Solution to this Two Column Geometric Proof practice problem is given in the video below!

## Shaded Area in a Square puzzle example question

In a unit square ABCD, point A is joined to the midpoint of BC, point B is joined to the midpoint of CD, point C is joined to the midpoint of DA, and point D is joined to the midpoint of AB. Find the area of the shaded region. Solution to this Puzzle practice problem is given in the video below!

## Shaded Area in a Square puzzle example problem

In a unit square ABCD, M is a midpoint of AD, and AC is a diagonal. Find the area of the shaded regions. Solution to this Puzzle practice problem is given in the video below!

## Shaded Area in a Square puzzle example

In the unit square ABCD, M is the midpoint and AC and BD are diagonals. Find the area of the shaded region. Solution to this Puzzle practice problem is given in the video below!

## Shaded Area in a Square puzzle example question

In the following unit square ABCD, M is the midpoint and BD is a diagonal. Find the area of the shaded region. Solution to this Puzzle practice problem is given in the video below!

## Shaded Area in a Square puzzle TRIGONOMETRY example problem

A square with side 1 is rotated around one vertex by an angle , where and .

Find the area of the shaded region. Solution to this Puzzle practice problem is given in the video below!

## Shaded Area in a Rectangle puzzle example

In the following rectangle, an isosceles triangle is drawn. Find the area of the shaded region. Solution to this Puzzle practice problem is given in the video below!

## Shaded Area in a Rectangle puzzle example question

In the following rectangle below, find the area of the shaded region. Solution to this Puzzle practice problem is given in the video below!

## Geometry problems (complete Playlist)

Explore a variety of Geometry examples and practice problems applicable to K-12, Precalculus or Calculus courses.