Ch. 7 Flashcards - English
HL ≅ (Hypotenuse-Leg congruence)
(Triangle Congruence) If the hypotenuse and one leg of one right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, the two right triangles are congruent. Note that this congruence condition applies only to right triangles.
ASA ≅ (Angle-Side-Angle Congruence
(Triangle Congruence) If two angles and the included side of one triangle are congruent to the corresponding two angles and included side of another triangle, the triangles are congruent.
AAS ≅ (Angle-Angle-Side Congruence)
(Triangle Congruence) If two pairs of corresponding angles and a pair of corresponding sides that are not between them have equal measure, then the triangles are congruent.
SSS ≅ (Side-Side-Side congruence)
(Triangle Congruence) Two triangles are congruent if all three pairs of corresponding sides are congruent.
SAS ≅ (Side-Angle-Side congruence)
(Triangle Congruence) Two triangles are congruent if two sides and their included angle of one triangle are congruent to the corresponding two sides and included angle of another triangle.
Flowchart
A diagram showing an argument for a conclusion from certain evidence. A flowchart uses ovals connected by arrows to show the logical structure of the argument. When each oval has a reason stated next to it showing how the evidence leads to that conclusion, the flowchart represents a proof.
Midpoint
A point that divides a segment into two segments of equal length. For example, point D is the midpoint of AB in ΔABC in the example below.
Midsegment
A segment joining the midpoints of two sides of a triangle. For example, DE is the midsegment of ΔABC
Polygon
A two-dimensional closed figure of three or more line segments (sides) connected end to end. Each segment is a side and only intersects the endpoints of its two adjacent sides. Each point of intersection is a vertex.
Triangle Congruence Condition
Conditions that use the minimum number of congruent corresponding parts to prove that two triangles are congruent. They are: SSS ≅, SAS ≅, AAS ≅, ASA ≅, and HL ≅.
Rigid Transformations
Movements of figures that preserve their shape and size. Examples of rigid transformations are reflections, rotations, and translations.
corresponding parts
Points, sides, edges, or angles in two or more figures that are images of each other with respect to a sequence of transformations. If two figures are congruent, their corresponding parts are congruent to each other.
Scale Factor
The ratio between a length of the representation (such as a map, model, or diagram) and the corresponding length of the actual object. It is written as the ratio of a length in the new figure (image) to a length in the original figure.
Coordinate Geometry
The study of geometry on a coordinate graph.
Triangle Angle Sum Theorem
The sum of the measures of the interior angles in any triangle is 180°.
Congruent
Two shapes are congruent if there is a sequence of rigid transformations that carries one onto the other. The corresponding angles and sides of congruent polygons have equal measures. Congruent shapes are similar and have a scale factor of 1. The symbol for congruent is ≅.
Similar
Two shapes are similar if there is a sequence of rigid motions, followed by a dilation, that carries one onto the other. The corresponding angles of similar polygons are congruent, and the corresponding sides are proportional. The symbol for similar is ~.