Podcast
Questions and Answers
What does the Congruent Complements Theorem state?
What does the Congruent Complements Theorem state?
- If two angles are supplementary to the same angle, then they are congruent.
- If two angles are complementary to the same angle, then they are congruent. (correct)
- If two angles are not complementary, then they are not congruent.
- If two angles are congruent, then they are complementary.
What does the Congruent Supplements Theorem state?
What does the Congruent Supplements Theorem state?
- If two angles are complementary to the same angle, then they are congruent.
- If two angles are supplementary to the same angle, then they are congruent. (correct)
- Two angles that are not supplementary cannot be congruent.
- Vertical angles are always congruent.
What does the Line Intersection Postulate state?
What does the Line Intersection Postulate state?
If two lines intersect, then their intersection is exactly one point.
What does the Linear Pair Postulate state?
What does the Linear Pair Postulate state?
What does the Line-Point Postulate state?
What does the Line-Point Postulate state?
What does the Plane-Point Postulate state?
What does the Plane-Point Postulate state?
What does the Plane Intersection Postulate state?
What does the Plane Intersection Postulate state?
What does the Plane-Line Postulate state?
What does the Plane-Line Postulate state?
All right angles are congruent.
All right angles are congruent.
What does the Two Point Postulate state?
What does the Two Point Postulate state?
What does the Three Point Postulate state?
What does the Three Point Postulate state?
Vertical angles are congruent.
Vertical angles are congruent.
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Study Notes
Congruent Complements Theorem
- States that if two angles are complementary to the same angle, or to congruent angles, then those two angles are congruent.
- Example: If angle 4 and angle 5 are complementary, and angle 6 and angle 5 are also complementary, then angle 4 is congruent to angle 6.
Congruent Supplements Theorem
- States that if two angles are supplementary to the same angle, or to congruent angles, then those angles are congruent.
- Example: If angle 1 and angle 2 are supplementary, and angle 3 and angle 2 are also supplementary, then angle 1 is congruent to angle 3.
Line Intersection Postulate
- If two lines intersect, their intersection consists of exactly one point.
- Example: The intersection of line m and line n occurs at point C.
Linear Pair Postulate
- States that if two angles form a linear pair, they are supplementary.
- Examples indicate that measures of angle 1 plus measures of angle 2 equal 180 degrees.
Line-Point Postulate
- A line must contain at least two points.
- Such as through any two distinct points A and B, there exists exactly one line l that includes these points.
Plane-Point Postulate
- A plane must contain at least three noncollinear points.
- Example: Through points D, E, F, there exists exactly one plane, referred to as plane R.
Plane Intersection Postulate
- If two planes intersect, their intersection forms a line.
- Example: The intersection of planes S and T is line l.
Plane-Line Postulate
- If two points are located within a plane, the line connecting those points also lies within the same plane.
- Example: If points D and E are within plane R, then line DE is also contained in plane R.
Right Angles Congruence Theorem
- States that all right angles measure the same, and thus are congruent.
Two Point Postulate
- Asserts that through any two points, there exists exactly one line.
- Similar to the Line-Point Postulate, exemplified by line l containing points A and B.
Three Point Postulate
- States that through any three noncollinear points, there exists exactly one plane.
- Shows that through points D, E, and F, the unique plane R can be established.
Vertical Angle Congruence Theorem
- Vertical angles, formed opposite each other when two lines intersect, are congruent.
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