Geometry Vocabulary and Theorems Quiz

Geometry Vocabulary

• Vocabulary words are: Nets, point, line, plane, collinear, noncollinear, coplanar, segment, ray, parallel, skew, parallel planes, congruent, angles, opposite rays, angle bisector, complementary angles, supplementary angles, linear pair, perpendicular lines, perpendicular bisector, vertical angles.

Theorems

• Segment addition
• Segment subtraction
• Distance Formula
• Midpoint formula
• Vertical Angles

Constructions

• Copy segment
• Copy angle
• Angle bisector
• Perpendicular bisector

Sample Problems

• Given ML is 68 units, find x, MV, and VL. MV = 3x - 10, and VL = 5x + 40.
• Use a figure to find the measure of different angles; example a, m∠ACD =, b. m∠FCE, c. m∠DCF =, d. m∠ACE =.
• The coordinates of the midpoint of AB are (5,6). The coordinates of A are (1, −6). Find the coordinates of B.
• Two supplementary angles are in the ratio of 4:5. Find the measure of each angle.
• In the figure (not drawn to scale), MO bisects ∠LMN, m∠LMO=18x-51 and m∠NMO=x+119. Solve for x and find m∠LMN
• Construct a right triangle, with the hypotenuse congruent to AB below.
• Using information on a diagram, prove BC=DE, given BD=CE
• Using information on a diagram, prove BC=DE, given BC=DE
• Given BC = DE, prove BD = CE
• Given BD = CE, prove BC=DE

Unit 2: Reasoning & Proof

• Vocabulary words: Deductive reasoning, postulates, axioms, theorems.

Theorems/Postulates

• Reflexive
• Substitution
• Transitive
• Addition
• Subtraction
• Halves of Equal quantities are equal
• All right angles are congruent
• Supplements of the same (congruent angles) are congruent
• Linear pairs are supplementary
• Complements of the same (congruent angles) are congruent
• Vertical Angles are congruent

Constructions

• Sample Problems

• Using the diagram of ABCD, prove AD-BC=CD, given AC=BD.

• Using the diagram of WXYZ, prove WX = YZ

• Using the information provided in the diagram, prove that two angles are congruent. Choose from supplementary angles, linear pairs of angles, or vertical angles.

Unit 3: Parallel & Perpendicular Lines

• Vocabulary: Transversal, alternate interior angles, alternate exterior angles, corresponding sides, same side interior angles, same side exterior angles, auxiliary line, slope

Theorems & Postulates

• Alternate interior angles are congruent ⇔ || lines
• Alternate exterior angles are congruent ⇔ || lines

Unit 4: Congruent Triangles

• Vocabulary: scalene, isosceles, equilateral, acute, right, obtuse, interior, exterior, remote interior angle, included side, included angle, vertex angle, base angle, legs

Theorems

• Sum of the interior angles of a triangle is 180.
• The measure of an exterior angle of a triangle is the sum of the remote interior angles.
• If two angles of a triangle are congruent to two angles of another triangle, the third angles are congruent.
• SSS, SAS, ASA, AAS, HL
• In a triangle sides opposite congruent angles are congruent.
• In a triangle, angles opposite congruent sides are congruent

Unit 5: Relationships in Triangles

• Vocabulary: concurrent, point of concurrency, circumscribed, inscribed, circumcenter, incenter, median, centroid, altitude, orthocenter, partition, directed segment, indirect proof

Theorems

• The perpendicular bisectors of the sides of the triangle are concurrent at a point equidistant from the vertices (circumcenter).
• The bisectors of the angles of a triangle are concurrent at a point equidistant from the sides of the triangle (incenter).
• The point of concurrency of the median of a triangle is the centroid which is ²½ the distance from the vertex on the median.
• The point of concurrency of the altitudes of the triangle is the orthocenter.
• Theorem: an exterior angle of a triangle is greater than either of its non-adjacent (remote) interior angles.
• In a triangle, the longest side is opposite the largest angle, the smallest side opposite the smallest angle.
• In a triangle the sum of two sides is greater than the length of the third side.

Constructions

• Perpendicular bisector
• Circumcenter
• Incenter
• Angle bisector
• Median
• Centroid
• Altitude
• Orthocenter
• Review the partition process
• Review Indirect Proofs
• Sample Problems

Unit 6: Quadrilaterals

• Vocabulary: regular polygon, quadrilateral, kite, trapezoid, parallelogram, rhombus, rectangle, square
• Theorems: The sum of the angles of any polygon is (n-2) 180. The sum of the exterior angles of a polygon is 360. Parts and extensions of parallel lines are parallel. If a parallelogram has one right angle, then it has four right angles. Properties of parallelograms, rectangle, rhombus, square, kite, trapezoid, isosceles trapezoid. Review coordinate proofs.
• Sample Problems