1st semester test Flashcards
30-60-90 triangle
A right triangle with interior angle measures of 30°, 60°, and 90°. In a 30-60-90 triangle, the hypotenuse is always twice as long as the shorter leg and the longer leg is √3 times as long as the shorter leg.
45-45-90 triangle
An isosceles right triangle with interior angle measures of 45°, 45°, and 90°. In a 45-45-90 triangle, the two legs have the same length and the hypotenuse is √2 times as long as either leg.
AA similarity postulate
A postulate stating that if two angles of one triangle are congruent to two angles of a second triangle, then the triangles are similar. AA stands for “angle-angle.”
AAS theorem
A theorem stating that if two angles and a nonincluded side of one triangle are congruent to the corresponding two angles and side of another, then the triangles are congruent. AAS stands for “angle-angle-side.”
acute angle
An angle that measures less than 90°. An acute angle is smaller than a right angle.
acute triangle
A triangle in which all three interior angles are acute.
adjacent
Next to each other. Two sides or two angles of a figure are adjacent if they are next to each other.
adjacent angles
Angles that share a vertex and one side.
alternate interior angles
Two angles formed by a line (called a transversal) that intersects two parallel lines. The angles are on opposite sides of the transversal and inside the parallel lines.
altitude of a triangle
The line segment from a vertex of a triangle that is perpendicular to the opposite side or to the line containing the opposite side.
angle
The object formed by two rays that share the same endpoint.
angle addition postulate
If point C lies in the interior of AVB, then mAVC + mCVB = mAVB.
angle bisector
A ray that divides an angle into two angles of equal measure.
angle of incidence
The angle between a ray of light meeting a surface and the line perpendicular to the surface at the point of contact.
angle of reflection
The angle between a ray of light reflecting off a surface and the line perpendicular to the surface at the point of contact.
angles
The corner-like spaces where the sides of a triangle meet.
arc
A part of the circumference of a circle. The symbol means “the arc with endpoints A and B.”
arc length
The length of an arc of a circle.
area
The space taken up by a two-dimensional figure or surface. Area is measured in square units, such as square inches, square centimeters, or square feet.
ASA
An acronym for “angle-side-angle.” These types of problems give you the measure of two angles in a triangle and the length of the side between those two angles. They can be solved using the law of sines.
ASA postulate
A postulate stating that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. ASA stands for “angle-side-angle.”
base
The side of the triangle that is perpendicular to the altitude.
base angles
The two angles formed by the base of a trapezoid and the two adjacent sides.
bases
The parallel sides of a trapezoid.
bisect
To divide into two equal parts.
center of dilation
The point from which a figure is scaled up or down in a dilation.
center of the circle
The point at the exact center of a circle. All points on a circle are the same distance from the center.
central angle
An angle that has its vertex at the center of a circle.
centroid
The point at which the three medians of a triangle intersect. The centroid of any triangle is inside the triangle.
chord
Any line segment whose endpoints are on the circle.
circle
A geometric figure consisting of all the points on a plane that are the same distance from a single point, called its center.
circumcenter of a triangle
The center of the only circle that can be circumscribed about a given triangle.
circumference
The distance around a circle.
circumscribed
Fit tightly around.
collinear
Lying in a straight line. Two points are always collinear. Three or more points are collinear if a straight line can be drawn through all of them.
common notion
A statement that is not officially defined but that is understood to be common sense.
complementary
Having angle measures that add up to 90°. If two complementary angles are adjacent, they form a right angle.
concave
Having one or more indentations. In math, a polygon is concave if a line can be drawn that contains a side of the polygon and also contains points inside the polygon.
conditional statement
A statement that has the form “If A, then B,” where A is what you assume is true and B is the conclusion.
congruence statement
A statement that tells which sides or angles of two triangles are congruent.
congruence transformation
An action that can be performed on a geometric object without changing its size or shape. Specific congruence transformations are rotations (turns), translations (slides), and reflections (flips).
congruent
Having the same size and shape. If polygons are congruent, their corresponding sides and angles are also congruent. The symbol means “congruent.”
congruent triangles
Triangles with all corresponding sides equal in length and all corresponding angles equal in measure. Congruent triangles have the exact same size and shape.
conjecture
A statement that appears to be correct based on observation but has not been proven or disproven
consecutive angles
Angles that are side-by-side.
consecutive interior angles
Two angles formed by a line (called a transversal) that intersects two parallel lines. The angles are on the same side of the transversal and are inside the parallel lines.
contrapositive
A statement in the form “If not B, then not A,” given the statement “If A, then B.”
converse
A statement in the form “If B, then A,” given the statement “If A, then B.”
coplanar
Lying in the same plane. Four or more points are coplanar if there is a plane that contains all of them.
corollary
A statement that makes sense based on a statement that has already been proven (that is, a theorem).
corresponding angles
Two nonadjacent angles formed on the same side of a line (called a transversal) that intersects two parallel lines, with one angle interior and one angle exterior to the lines.
cosine
In a right triangle, the ratio of the length of the angle’s adjacent leg to the length of the hypotenuse. Its abbreviation is cos.
CPCTC
An abbreviation that stands for “corresponding parts of congruent triangles are congruent.” If two triangles are congruent, each side or angle of one triangle is congruent to the corresponding side or angle of the other triangle.
decagon
A polygon with 10 sides.
deduction
A way of thinking that starts with a given set of rules and conditions and figures out what must be true based on what is given.
definition
A statement that describes the qualities of an idea, object, or process.
diagonal
A line segment that connects two nonconsecutive vertices of a polygon.
diameter
A line segment that contains the center of the circle and has endpoints on the circle. This term also refers to the length of this line segment; the diameter of a circle is twice the radius.
dilate
To change the size but not the shape of a geometric figure. The resulting figure is similar to the original but is not congruent to it. A dilation stretches or shrinks the original figure by a certain scale factor in relation to a point called the center of dilation.
endpoint
A point at the end of a ray, either end of a line segment, or either end of an arc.
equilateral triangle
A triangle with three sides of equal length. The three angles of an equilateral triangle each measure 60°.
exterior angles
Angles on the outside of a triangle that form linear pairs with interior angles of the triangle.
Angles that are on the outside of a polygon and form linear pairs with interior angles of the polygon.
flowchart proof
A type of proof that uses a graphical representation. Statements are placed in boxes, and the justification for each statement is written under the box. Arrows indicate the logical flow of the statements.
HA congruence theorem
A theorem stating that if the hypotenuse and an acute angle of one right triangle are congruent to the hypotenuse and corresponding acute angle of another right triangle, then the right triangles are congruent. HA stands for “hypotenuse-angle.”
HL congruence theorem
A theorem stating that if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the right triangles are congruent. HL stands for “hypotenuse-leg.”
