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Name ____________________________ Date __________ Period _____ ANY DEFINITION WITH BLANKS WILL BE TESTED! GEOMETRY VOCABULARY – UNIT 1 Together, let’s express the definition of each term by filling in the blanks. Term Ch 1 Section 1 POINT LINE COLLINEAR PLANE COPLANAR LINE SEGMENT RAY ENDPOINT POSTULATE Description Diagram Collinear points lie on the same line . A plane is a flat surface that has no thickness and infinitely extends in all directions. Points or lines that lie on the same plane are called coplanar. A line segment is a straight path that begins at one point and ends at another point. It has a finite length A straight path that has a beginning but no end is called a ray. A point that begins or ends a line segment or begins a ray is called an endpoint A statement we are asked to accept as true is called a postulate (or axiom). How to Name It Use the word point and a capital letter. A point names a location in 2 or 3 dimensions. It has NO size. A line is a straight path that has no thickness and infinitely extends in both directions. G2A Point P Plot Point C so it’s collinear with points A & Z. Use a script cap: Plane V, or three coplanar points Plane FGH MORE GEOMETRY VOCABULARY – UNIT 1 Term OPPOSITE RAYS Ch 1 Section 2 CONSTRUCTION BETWEEN COORDINATES DISTANCE /LENGTH CONGRUENT SEGMENTS BISECT MIDPOINT SEGMENT BISECTOR PAGE 2 Description Opposite rays share a common endpoint form a straight line, pointing in opposite directions. Construction is the process we use to create precise figures and diagrams. A point lies between two other points if all 3 points are collinear. The markings on a ruler used to measure line segments are the coordinates of the ruler. Distance or length is the absolute value of the difference between two coordinates. Line segments that are the same length are congruent segments. To bisect a segment is to divide it into two congruent pieces. A midpoint is a point that bisects a line segment. A segment bisector is any point, line, line segment, ray, or plane that bisects a line segment. Diagram Plot Points A & Z to create opposite rays. How to Name It We need an endpoint to start to name any ray. MORE GEOMETRY VOCABULARY – UNIT 1 Term Ch 1 Section 3 ANGLE VERTEX of an ANGLE INTERIOR/EXTERIOR OF AN ANGLE DEGREE MEASURE ACUTE ANGLE RIGHT ANGLE OBTUSE ANGLE STRAIGHT ANGLE Page 3 Description An angle is a figure formed by two rays with a common endpoint The vertex of an angle is found at the common endpoint of the two rays forming the angle. The interior of an angle is between the rays forming the angle. The exterior of an angle is outside the rays forming the angle. The measurement of 1/360 th of the one rotation it takes to form a circle is called a degree. Angle measure reveals how close an angle is to the 360O rotation of a complete circle . Therefore, angles are measured in degrees An acute angle has a measure between 0 and 90. A right angle has a measure of exactly 90 . An obtuse angle has a measure between 90 and 180. A straight angle has a measure of exactly 180 . Hang In There, Still More … Diagram How to Name It There are 4 ways to name the angle below: its unique vertex: Y by number: 2 the vertex and point on each side: XYZ or ZYX MORE GEOMETRY VOCABULARY – UNIT 1 Term CONGRUENT ANGLES ANGLE BISECTOR Ch 1 Section 4 ADJACENT ANGLES LINEAR PAIR COMPLEMENTARY ANGLES SUPPLEMENTARY ANGLES VERTICAL ANGLES Page 4 Description Congruent angles have the same measurement. A ray, line or line segment that divides an angle into two congruent angles is called an angle bisector. Adjacent angles share a common side. They lay next to each other without any gaps. Linear pairs are adjacent angles that form a straight angle of 180 . The measures of two Diagram How to Name It 5 Why are 4 & 5 NOT a linear pair? complementary angles Which pair are supplementary? supplementary angles Complementary? sum to 90 . The measures of two sum to 180 . When two lines intersect , the two angles opposite each other are called vertical angles. MORE GEOMETRY VOCABULARY – UNIT 1 Page 5 Ch 1 Section 5 COORDINATE PLANE COORDINATE Ch 3 Section 1 PARALLEL LINES Are Coplanar and do not Intersect . (Note that parallel lines have arrows in line l || line m the middle of them.) PERPENDICULAR LINES SKEW LINES Intersect at 90o Are lines which do not AND are NOT angles. Intersect Coplanar line k line l line k is skew to line m Since lines PARALLEL PLANES Are planes which do not Intersect l and m are parallel lines which lie on planes . P and R, then planes P and R are parallel planes. l P m R STILL MORE GEOMETRY VOCABULARY – UNIT 1 Page 6 Ch 3 Section 3 TRANSVERSAL A Line which intersects other lines at different Lie on the CORRESPONDING ANGLES ALTERNATE EXTERIOR ANGLES SAME-SIDE INTERIOR ANGLES Points . Same Side of the transversal and the Same Side of the other two lines. Lie on ALTERNATE INTERIOR ANGLES Two 1 2 3 4 & & & & 5 6 7 8 Opposite sides of the transversal and Inside of Lie on the Line t is a transversal for lines a & b the other two lines. 4 & 5 3 & 6 Opposite side of the transversal and Outside the other two lines. Lie on the 2 & 7 1 & 8 Same Side of the transversal and Inside the other two lines. 4 & 6 3 & 5 WHAT!! … MORE GEOMETRY VOCABULARY – UNIT 1 Ch 4 Section 1 TRIANGLE Any triangle with 3 acute angles. EQUIANGULAR TRIANGLE Any triangle with 3 congruent angles. RIGHT TRIANGLE Any triangle with 1 right angle. OBTUSE TRIANGLE Any triangle with 1 obtuse angle. EQUILATERAL TRIANGLE Any triangle with 3 congruent sides. ACUTE ISOSCELES TRIANGLE LEGS OF AN ISOSCELES TRIANGLE BASE OF AN ISOSCELES TRIANGLE Page 7 Any triangle with at least 2 congruent sides (or angles). The 2 congruent legs of an isosceles triangle. The base is the non- congruent side of an isosceles triangle. BASE ANGLES OF The 2 angles opposite the legs AN ISOSCELES TRIANGLE of an isosceles triangle. The legs of the isosceles triangle measures ____ units. Mark the base of the isosceles triangle with one tic mark Place double arc marks on the base angles of the isosceles triangle. ALMOST THERE … MORE GEOMETRY VOCABULARY – UNIT 1 SCALENE TRIANGLE Ch 4 Section 2 INTERIOR ANGLE Any triangle with no congruent sides. Any angle formed by two sides of a triangle. Any angle formed by one side of the triangle and EXTERIOR ANGLE REMOTE INTERIOR ANGLES Page 8 extending another side of the triangle. An interior angle that is not adjacent to the exterior angle. 2, 3 & 5 are interior angles. OF COURSE … MORE GEOMETRY VOCABULARY – UNIT 1 Page 9 Ch 6 Section 1 A closed 2-D figure formed polygon polygon ABCDEF by 3 or more line segments. Any line segment side of a polygon B C side EF that forms a polygon. (adjacent vertices) Any common endpoint of two vertex of a polygon A vertex point D interior angle D sides of a polygon. F diagonal D Any line segment which connects two non-adjacent vertices. Any polygon which is BOTH regular polygon equilateral and equiangular. irregular polygon Any polygon which is NOT BOTH equilateral and equiangular The End … ? Nope E diagonal AC STILL MORE GEOMETRY VOCABULARY – UNIT 1 convex polygon concave polygon Undefined Term Page 10 Any polygon where all diagonals lie inside of the polygon. Any polygon with at least one diagonal lies outside of the polygon. The 3 undefined terms of geometry are points, lines and planes because they cannot be defined from other figures. Other figures are defined based upon points, lines and planes.