Podcast
Questions and Answers
Which of the following describes a pair of lines that never intersect and are always the same distance apart?
Which of the following describes a pair of lines that never intersect and are always the same distance apart?
What is the relationship between vertical angles?
What is the relationship between vertical angles?
In a right triangle, if one angle measures 30 degrees, what is the measure of the other acute angle?
In a right triangle, if one angle measures 30 degrees, what is the measure of the other acute angle?
What is the purpose of an angle bisector?
What is the purpose of an angle bisector?
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Which of the following is NOT a postulate related to angle relationships?
Which of the following is NOT a postulate related to angle relationships?
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Which formula is used to determine the distance between two points in a coordinate plane?
Which formula is used to determine the distance between two points in a coordinate plane?
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What is the measure of each angle in a pair of supplementary angles that are in the ratio of 2:3?
What is the measure of each angle in a pair of supplementary angles that are in the ratio of 2:3?
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What type of reasoning utilizes general principles to arrive at a specific conclusion?
What type of reasoning utilizes general principles to arrive at a specific conclusion?
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Which construction involves creating a segment that is perpendicular to a given line at a specific point?
Which construction involves creating a segment that is perpendicular to a given line at a specific point?
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What is the measure of an angle that is complementary to a 35-degree angle?
What is the measure of an angle that is complementary to a 35-degree angle?
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Which of the following statements about alternate angles and parallel lines is true?
Which of the following statements about alternate angles and parallel lines is true?
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What is the relationship between the slopes of two perpendicular lines?
What is the relationship between the slopes of two perpendicular lines?
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In a triangle, if two angles are congruent, what can be inferred about the third angle?
In a triangle, if two angles are congruent, what can be inferred about the third angle?
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What is true about the sum of the interior angles of a triangle?
What is true about the sum of the interior angles of a triangle?
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If two coplanar lines are perpendicular to the same line, what can be concluded about the two lines?
If two coplanar lines are perpendicular to the same line, what can be concluded about the two lines?
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What type of triangle is characterized by having all sides of different lengths?
What type of triangle is characterized by having all sides of different lengths?
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Which theorem states that the measure of an exterior angle of a triangle is equal to the sum of the remote interior angles?
Which theorem states that the measure of an exterior angle of a triangle is equal to the sum of the remote interior angles?
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When two lines are parallel, what can be said about their slopes?
When two lines are parallel, what can be said about their slopes?
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What is the relationship between same side exterior angles formed by a transversal cut through two parallel lines?
What is the relationship between same side exterior angles formed by a transversal cut through two parallel lines?
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In a triangle, what can be said about the lengths of the sides opposite the angles?
In a triangle, what can be said about the lengths of the sides opposite the angles?
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What characteristic is unique to a rhombus compared to a rectangle?
What characteristic is unique to a rhombus compared to a rectangle?
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Which statement accurately describes a trapezoid?
Which statement accurately describes a trapezoid?
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Which property is true for all squares?
Which property is true for all squares?
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What is a defining property of kites?
What is a defining property of kites?
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Which of the following best defines an isosceles trapezoid?
Which of the following best defines an isosceles trapezoid?
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What is true about the angles of a rectangle?
What is true about the angles of a rectangle?
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In what way are the diagonals of a square similar to those of a rhombus?
In what way are the diagonals of a square similar to those of a rhombus?
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Which condition must be met for a quadrilateral to be considered a parallelogram?
Which condition must be met for a quadrilateral to be considered a parallelogram?
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How do the diagonals behave in a rectangle?
How do the diagonals behave in a rectangle?
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What is true about the interior angles of a regular hexagon?
What is true about the interior angles of a regular hexagon?
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What is the point of concurrency for the angle bisectors of a triangle called?
What is the point of concurrency for the angle bisectors of a triangle called?
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Which theorem states that an exterior angle of a triangle is greater than either of its non-adjacent interior angles?
Which theorem states that an exterior angle of a triangle is greater than either of its non-adjacent interior angles?
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If a triangle has a median, what point of concurrency does this median create?
If a triangle has a median, what point of concurrency does this median create?
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What is true regarding the sides and angles of a triangle?
What is true regarding the sides and angles of a triangle?
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What is the relationship between the sum of the interior angles of an n-sided polygon?
What is the relationship between the sum of the interior angles of an n-sided polygon?
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What point of a triangle is the intersection point of the altitudes?
What point of a triangle is the intersection point of the altitudes?
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Which of the following statements is false regarding parallelograms?
Which of the following statements is false regarding parallelograms?
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Which construction is used to determine the circumcenter of a triangle?
Which construction is used to determine the circumcenter of a triangle?
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In a triangle, the centroid divides each median into what ratio?
In a triangle, the centroid divides each median into what ratio?
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What is the sum of the exterior angles of any polygon?
What is the sum of the exterior angles of any polygon?
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Study Notes
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
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Sample Problems
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Using the diagram of ABCD, prove AD-BC=CD, given AC=BD.
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Using the diagram of WXYZ, prove WX = YZ
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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
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Description
Test your knowledge of essential geometry vocabulary, theorems, and constructions. This quiz includes segment addition, distance formula, and angle relationships through sample problems. Challenge yourself and reinforce your understanding of foundational concepts in geometry.
