1st semester test

Question 1

30-60-90 triangle

Answer 1

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.

Question 2

45-45-90 triangle

Answer 2

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.

Question 3

AA similarity postulate

Answer 3

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.”

Question 4

AAS theorem

Answer 4

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.”

Question 5

acute angle

Answer 5

An angle that measures less than 90°. An acute angle is smaller than a right angle.

Question 6

acute triangle

Answer 6

A triangle in which all three interior angles are acute.

Question 7

adjacent

Answer 7

Next to each other. Two sides or two angles of a figure are adjacent if they are next to each other.

Question 8

adjacent angles

Answer 8

Angles that share a vertex and one side.

Question 9

alternate interior angles

Answer 9

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.

Question 10

altitude of a triangle

Answer 10

The line segment from a vertex of a triangle that is perpendicular to the opposite side or to the line containing the opposite side.

Question 11

angle

Answer 11

The object formed by two rays that share the same endpoint.

Question 12

angle addition postulate

Answer 12

If point C lies in the interior of AVB, then mAVC + mCVB = mAVB.

Question 13

angle bisector

Answer 13

A ray that divides an angle into two angles of equal measure.

Question 14

angle of incidence

Answer 14

The angle between a ray of light meeting a surface and the line perpendicular to the surface at the point of contact.

Question 15

angle of reflection

Answer 15

The angle between a ray of light reflecting off a surface and the line perpendicular to the surface at the point of contact.

Question 16

angles

Answer 16

The corner-like spaces where the sides of a triangle meet.

Question 17

arc

Answer 17

A part of the circumference of a circle. The symbol means “the arc with endpoints A and B.”

Question 18

arc length

Answer 18

The length of an arc of a circle.

Question 19

area

Answer 19

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.

Question 20

ASA

Answer 20

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.

Question 21

ASA postulate

Answer 21

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.”

Question 22

base

Answer 22

The side of the triangle that is perpendicular to the altitude.

Question 23

base angles

Answer 23

The two angles formed by the base of a trapezoid and the two adjacent sides.

Question 24

bases

Answer 24

The parallel sides of a trapezoid.

Question 25

bisect

Answer 25

To divide into two equal parts.

Question 26

center of dilation

Answer 26

The point from which a figure is scaled up or down in a dilation.

Question 27

center of the circle

Answer 27

The point at the exact center of a circle. All points on a circle are the same distance from the center.

Question 28

central angle

Answer 28

An angle that has its vertex at the center of a circle.

Question 29

centroid

Answer 29

The point at which the three medians of a triangle intersect. The centroid of any triangle is inside the triangle.

Question 30

chord

Answer 30

Any line segment whose endpoints are on the circle.

Question 31

circle

Answer 31

A geometric figure consisting of all the points on a plane that are the same distance from a single point, called its center.

Question 32

circumcenter of a triangle

Answer 32

The center of the only circle that can be circumscribed about a given triangle.

Question 33

circumference

Answer 33

The distance around a circle.

Question 34

circumscribed

Answer 34

Fit tightly around.

Question 35

collinear

Answer 35

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.

Question 36

common notion

Answer 36

A statement that is not officially defined but that is understood to be common sense.

Question 37

complementary

Answer 37

Having angle measures that add up to 90°. If two complementary angles are adjacent, they form a right angle.

Question 38

concave

Answer 38

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.

Question 39

conditional statement

Answer 39

A statement that has the form "If A, then B," where A is what you assume is true and B is the conclusion.

Question 40

congruence statement

Answer 40

A statement that tells which sides or angles of two triangles are congruent.

Question 41

congruence transformation

Answer 41

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).

Question 42

congruent

Answer 42

Having the same size and shape. If polygons are congruent, their corresponding sides and angles are also congruent. The symbol means "congruent."

Question 43

congruent triangles

Answer 43

Triangles with all corresponding sides equal in length and all corresponding angles equal in measure. Congruent triangles have the exact same size and shape.

Question 44

conjecture

Answer 44

A statement that appears to be correct based on observation but has not been proven or disproven

Question 45

consecutive angles

Answer 45

Angles that are side-by-side.

Question 46

consecutive interior angles

Answer 46

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.

Question 47

contrapositive

Answer 47

A statement in the form "If not B, then not A," given the statement "If A, then B."

Question 48

converse

Answer 48

A statement in the form "If B, then A," given the statement "If A, then B."

Question 49

coplanar

Answer 49

Lying in the same plane. Four or more points are coplanar if there is a plane that contains all of them.

Question 50

corollary

Answer 50

A statement that makes sense based on a statement that has already been proven (that is, a theorem).

Question 51

corresponding angles

Answer 51

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.

Question 52

cosine

Answer 52

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.

Question 53

CPCTC

Answer 53

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.

Question 54

decagon

Answer 54

A polygon with 10 sides.

Question 55

deduction

Answer 55

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.

Question 56

definition

Answer 56

A statement that describes the qualities of an idea, object, or process.

Question 57

diagonal

Answer 57

A line segment that connects two nonconsecutive vertices of a polygon.

Question 58

diameter

Answer 58

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.

Question 59

dilate

Answer 59

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.

Question 60

endpoint

Answer 60

A point at the end of a ray, either end of a line segment, or either end of an arc.

Question 61

equilateral triangle

Answer 61

A triangle with three sides of equal length. The three angles of an equilateral triangle each measure 60°.

Question 62

exterior angles

Answer 62

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.

Question 63

flowchart proof

Answer 63

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.

Question 64

HA congruence theorem

Answer 64

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."

Question 65

HL congruence theorem

Answer 65

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."