Lines, Angles, & Triangles - SAT Math

Area = $\frac{1}{2} \times \text{base} \times \text{height}$. Standard formula using base and perpendicular height.

180 degrees. This is a fundamental property that applies to all triangles.

Exterior angle = sum of two remote interior angles. An exterior angle equals the sum of the two non-adjacent interior angles.

$a^2 + b^2 = c^2$. Relates the sides of a right triangle: legs squared equal hypotenuse squared.

60 degrees. Each exterior angle of a regular hexagon: $360° ÷ 6 = 60°$.

360 degrees. Any quadrilateral's interior angles sum to $360°$.

80 degrees. Triangle angles sum to $180°$: $180° - 45° - 55° = 80°$.

Special right triangle. Has angle measures in the ratio $1:2:3$ or $30°:60°:90°$.

Supplementary angles. Two angles whose measures add up to $180°$.

60 degrees. Each angle in an equilateral triangle measures $180° ÷ 3 = 60°$.

Diagonal. Connects two vertices that are not adjacent (next to each other).

$\frac{1}{2} \times \text{base} \times \text{height}$. Multiply base by height, then divide by 2.

They are equal. Vertical angles are formed when two lines intersect and are always congruent.

Equilateral triangle. All three sides have the same length.

$\frac{1}{2} \times \text{leg}_1 \times \text{leg}_2$. The two legs are perpendicular, so multiply and divide by 2.

60 degrees. Since all angles are equal and sum to $180°$, each is $180° ÷ 3 = 60°$.

Right triangle. Contains exactly one $90°$ angle.

The right angle (90 degrees). The largest angle is always opposite the longest side (hypotenuse).

5 units. Using Pythagorean theorem: $\sqrt{3^2 + 4^2} = \sqrt{25} = 5$.

Complementary angles. Two angles whose measures add up to $90°$.

Alternate interior angles are equal. When parallel lines are cut by a transversal, alternate interior angles are congruent.

Scalene triangle. All three sides have different lengths.

Triangle Sum Theorem. States that interior angles of any triangle sum to $180°$.

Median. Connects a vertex to the midpoint of the opposite side.

5√3. In a 30-60-90 triangle, longer leg = hypotenuse × $\frac{\sqrt{3}}{2}$.

They are equal. When parallel lines are cut by a transversal, corresponding angles are congruent.

24 square units. Area = $\frac{1}{2} \times 6 \times 8 = 24$ square units.

Angle bisector. Divides an angle into two congruent angles.

Isosceles right triangle. Has two $45°$ angles and one $90°$ angle with two equal legs.

They are supplementary. Consecutive interior angles on the same side of a transversal sum to $180°$.

60 degrees. Triangle angles sum to $180°$: $180° - 70° - 50° = 60°$.

Line. Has no endpoints and extends infinitely in both directions.

Sum of all sides. Add the lengths of all three sides together.

Vertical angles. Opposite angles formed when two lines intersect are called vertical angles.

Two sides of equal length. Has exactly two sides of equal length and two equal angles.

360 degrees. This applies to all polygons, regardless of number of sides.

Obtuse triangle. Contains one angle greater than $90°$ but less than $180°$.

$7\text{√2}$. In 45-45-90 triangles, hypotenuse = leg × $\sqrt{2}$.

Adjacent angles. Share a common vertex and a common side but no interior points.

Acute triangle. All three angles measure less than $90°$.

Area = $\frac{1}{2} \times \text{base} \times \text{height}$. Multiply base by height, then divide by 2 for triangle area.

$x = 70$ degrees. Triangle angles sum to $180°$: $50° + 60° + x = 180°$.

$a^2 + b^2 = c^2$. Relates the sides of a right triangle: legs squared equal hypotenuse squared.

They are equal. Angles formed by intersecting lines across from each other are congruent.

Equilateral triangle. All three sides congruent means all angles are $60°$ each.

60 degrees. Triangle angles sum to $180°$: $40° + 80° + x = 180°$.

Sum = $(n-2) \times 180$ degrees. For $n$ sides, subtract 2 then multiply by $180°$.

A triangle with two equal sides. Two equal sides create two equal base angles in the triangle.

180 degrees. This is a fundamental property of triangles in Euclidean geometry.

A triangle with one 90-degree angle. The right angle distinguishes it from acute and obtuse triangles.

180 degrees. This is a fundamental property of all triangles in Euclidean geometry.

Base angles are equal. The two angles opposite the equal sides are congruent.