Geometry EOC

What is the outcome of dilating a coordinate by a scale factor greater than 1?

An enlargement is produced.

What happens to ordered pairs when translated ' S units to the left and 4 units up'?

The mapping is (x,y) → (x - S,y + 4).

What is the result of rotating the ordered pairs (x, y) 90°?

The ordered pairs change to (-y, x).

How are the ordered pairs affected when reflecting over the x-axis?

They change from (x, y) to (x, -y).

What conditions must be met for three sides to form a triangle?

The sum of the two smallest sides must be greater than the third side.

What defines a right triangle?

A triangle with one 90° angle and two acute angles.

In an isosceles triangle, what is true about the base angles?

The base angles are equal.

How do you identify the largest angle in a triangle?

It is across from the longest side.

What is a defining property of equilateral triangles?

All sides and angles are congruent.

What happens when ordered pairs are rotated 360°?

The ordered pairs stay the same.

Describe a property of squares in relation to their angles and sides.

All angles are 90° and all sides are equal.

How do the ordered pairs change when reflecting over the line y = x?

They change from (x, y) to (y, x).

What is the median of a trapezoid?

The median is ½ the sum of the lengths of the bases.

What characterizes a triangle as acute?

All angles are less than 90°.

What is the relationship between the angles in an equiangular triangle?

All angles are congruent, and each measures 60°.

What is the requirement for a scale factor when a figure is congruent to its pre-image?

The scale factor must equal 1.

What changes occur when rotating (x, y) 180°?

The ordered pairs change to (-x, -y).

In the context of triangle inequalities, what does the Pythagorean Theorem determine?

It determines if three sides can form a right triangle.

What must the longest side of a right triangle be in relation to the other sides when using the Pythagorean Theorem?

It must be substituted in for c.

What is true about the diagonals of rectangles?

They are equal and bisect each other.

How do you find the length of the third side of a triangle given two sides?

The length must be between the difference and the sum of the two given sides.

What shape has opposite sides equal and consecutive angles supplementary?

A parallelogram.

What is the characteristic of a rhombus regarding its diagonals?

The diagonals bisect each other at right angles.

What is a defining property of trapezoids?

At least one pair of opposite sides is parallel.

In transformations, what effect does a scale factor between 0 and 1 have?

It produces a reduction.

What is the outcome of dilating a coordinate by a scale factor greater than 1?

An enlargement is produced.

What happens to ordered pairs when translated ' S units to the left and 4 units up'?

The mapping is (x,y) → (x - S,y + 4).

What is the result of rotating the ordered pairs (x, y) 90°?

The ordered pairs change to (-y, x).

How are the ordered pairs affected when reflecting over the x-axis?

They change from (x, y) to (x, -y).

What conditions must be met for three sides to form a triangle?

The sum of the two smallest sides must be greater than the third side.

What defines a right triangle?

A triangle with one 90° angle and two acute angles.

In an isosceles triangle, what is true about the base angles?

The base angles are equal.

How do you identify the largest angle in a triangle?

It is across from the longest side.

What is a defining property of equilateral triangles?

All sides and angles are congruent.

What happens when ordered pairs are rotated 360°?

The ordered pairs stay the same.

Describe a property of squares in relation to their angles and sides.

All angles are 90° and all sides are equal.

How do the ordered pairs change when reflecting over the line y = x?

They change from (x, y) to (y, x).

What is the median of a trapezoid?

The median is ½ the sum of the lengths of the bases.

What characterizes a triangle as acute?

All angles are less than 90°.

What is the relationship between the angles in an equiangular triangle?

All angles are congruent, and each measures 60°.

What is the requirement for a scale factor when a figure is congruent to its pre-image?

The scale factor must equal 1.

What changes occur when rotating (x, y) 180°?

The ordered pairs change to (-x, -y).

In the context of triangle inequalities, what does the Pythagorean Theorem determine?

It determines if three sides can form a right triangle.

What must the longest side of a right triangle be in relation to the other sides when using the Pythagorean Theorem?

It must be substituted in for c.

What is true about the diagonals of rectangles?

They are equal and bisect each other.

How do you find the length of the third side of a triangle given two sides?

The length must be between the difference and the sum of the two given sides.

What shape has opposite sides equal and consecutive angles supplementary?

A parallelogram.

What is the characteristic of a rhombus regarding its diagonals?

The diagonals bisect each other at right angles.

What is a defining property of trapezoids?

At least one pair of opposite sides is parallel.

In transformations, what effect does a scale factor between 0 and 1 have?

It produces a reduction.

What is the Pythagorean Theorem and how does it work?

$a^2 + b^2 = c^2$, where $a$ and $b$ are the lengths of the legs, and $c$ is the length of the hypotenuse.

What is the formula for the area of a circle?

Area = $πr^2$, where $r$ is the radius of the circle.

What is the formula for the volume of a rectangular prism?

Volume = $lwh$, where $l$ is the length, $w$ is the width, and $h$ is the height.

How do you calculate the surface area of a rectangular prism?

Surface Area = $2(lw + lh + wh)$.

What is the

Area = $1/2 * b * h$, where $b$ is the length of the base, and $h$ is the height from the base to the opposite vertex.