Definitions of Geometric Terms Definitions RAY RAY Defined

Definitions of Geometric Terms

Definitions RAY: RAY Defined as …Ray AB is part of line AB that contains Point A and all the points on line AB that are on the same side of point A as point B. Ray AB has an endpoint of A; B A Ray AB

Definitions Take Note! These are two different rays!

Definitions Name a ray in two ways.

Definitions Two rays that share a common endpoint, provided that the two rays do not lie on the same line. The common endpoint of the ANGLE: ANGLE two rays that make an angle is the vertex of the angle. The two rays are called the sides of the angle. Side A Vertex A How do we name angles?

Definitions MEASURE OF AN ANGLE: ANGLE The smallest amount of rotation for a ray to move from the overlapping position to the final position In DEGREES 115 o 28. 6 o How do write an angle’s measure in symbol form?

Definitions CONGRUENT: CONGRUENT Two geometric figures are congruent if and only if they are identical in shape and size. 40 o Are these congruent even if they point to different directions? 40 o

Definitions CONGRUENT ANGLES: ANGLES Two angles are congruent angles if and only if they have the same measure. 40 o

Definitions ACUTE ANGLE: ANGLE An angle whose measure is less than 90 o 95 o 30 o 40 o 50 o

Definitions ACUTE ANGLE: ANGLE An angle whose measure is less than 90 o 60 o 95 o 30 o Is the angle formed by 2 segments acute? 40 o 50 o

Definitions RIGHT 75 o ANGLE: ANGLE An angle whose measure is 90 o 40 o 90 o 126 o 2 intersecting lines can form angles. 90 o

Definitions OBTUSE ANGLE: ANGLE An angle whose measure is greater than 90 o 30 o 40 o 95 o 60 o 130 o 155 o

Definitions ANGLE BISECTOR: BISECTOR A ray that has an endpoint on the vertex of an angle and that divides the angle into two angles of equal measure. D A What ray bisects Angle ABC? 60 o B Ray BD. E 60 o C

Definitions ANGLE BISECTOR: BISECTOR A ray that has an endpoint on the vertex of an angle and that divides the angle into two angles of equal measure. D Is the green ray an angle bisector of Angle ABE? No. The ray does not share the vertex of angle ABE. A 60 o B E 60 o C

Definitions PARALLEL LINES: LINES Two coplanar lines that do not intersect.

Definitions COMPLEMENTARY ANGLES: ANGLES Two angles whose measures have the sum of 90 o. Pairs of Complementary Angles

Definitions VERTICAL ANGLES: ANGLES If Line AB and Line CD intersect at point P so that point P is between points A and B and also between points C and D, then APC and BPD are a pair of vertical angles. Angles APD and BPC are also a pair of vertical angles. D P A B C Common vertex

Definitions W G R F P X S H Pairs of Vertical Angles: G and R; W and P; X and T; S and H B T Are these pairs of Vertical Angles: B and F? Z and K? J and A? Z J A K

Definitions PERPENDICULAR LINES: LINES Two lines that intersect to form a right angle. Line J A right angle is an angle whose measure is 90 degrees. Therefore, perpendicular lines form angles of 90 degree measures. Line B

Definitions PERPENDICULAR LINES: LINES Two lines that intersect to form a right angle. 90 o Are intersecting lines always perpendicular? No. Can we call the green segments as perpendicular segments?

Definitions SUPPLEMENTARY ANGLES: ANGLES Two angles whose measures have the sum of 180 o. A M 95 o 70 o D Pairs of Supplementary Angles 110 o G 85 o 30 o 150 o

Definitions LINEAR PAIR OF ANGLES: ANGLES If X, Y, and Z are consecutive collinear points and W is a point not on Line XZ, then XYW and WYZ form a linear pair of angles. W X Y Collinear points Z

Definitions LINEAR PAIR OF ANGLES: ANGLES 2 angles form a linear pair if they share the same vertex, share same sides, and whose non-shared sides form a line. Shared sides G Non-Shared sides H Common Vertex