Podcast
Questions and Answers
What does the SSS postulate refer to in congruent triangles?
What does the SSS postulate refer to in congruent triangles?
- Two angles and the included side must be equal.
- The hypotenuse and one leg must be equal.
- Two angles and a side must be equal.
- Three sides of one triangle are congruent to three sides of another triangle. (correct)
Which postulate uses an included angle to establish congruence?
Which postulate uses an included angle to establish congruence?
- SAS (correct)
- AAS
- ASA
- HL
In which postulate is the hypotenuse and one leg of a right triangle used?
In which postulate is the hypotenuse and one leg of a right triangle used?
- ASA
- HL (correct)
- SAS
- AAS
Which of the following describes the AAS postulate?
Which of the following describes the AAS postulate?
Which congruence criterion does NOT require a side to be included between two angles?
Which congruence criterion does NOT require a side to be included between two angles?
What type of angles are ∠10 and ∠14 if they share a common vertex and side?
What type of angles are ∠10 and ∠14 if they share a common vertex and side?
Which angles are considered alternate interior angles?
Which angles are considered alternate interior angles?
If two angles sum up to 180°, what type of angles are they?
If two angles sum up to 180°, what type of angles are they?
What are same-side exterior angles?
What are same-side exterior angles?
Which of the following angles are complementary?
Which of the following angles are complementary?
What defines two triangles as being congruent?
What defines two triangles as being congruent?
If triangle ABC is congruent to triangle PQR, what is true about the angles?
If triangle ABC is congruent to triangle PQR, what is true about the angles?
Which of the following statements about corresponding parts of congruent triangles is true?
Which of the following statements about corresponding parts of congruent triangles is true?
How should the triangles be labeled to show congruence properly?
How should the triangles be labeled to show congruence properly?
What can be concluded if ∆ABC ≅ ∆XYZ?
What can be concluded if ∆ABC ≅ ∆XYZ?
What defines two lines as parallel?
What defines two lines as parallel?
Which of the following terms describes a line that intersects two or more lines at different points?
Which of the following terms describes a line that intersects two or more lines at different points?
Which angles are located inside two parallel lines?
Which angles are located inside two parallel lines?
How are perpendicular lines represented?
How are perpendicular lines represented?
What is the common term for angles that are opposite each other when two lines intersect?
What is the common term for angles that are opposite each other when two lines intersect?
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Study Notes
Angle Definition
- An angle is made by two rays meeting at a point, the vertex.
- This angle can be named in different ways, e.g., ∠ACB, ∠BCA, or ∠C.
- The sides of the angle are the rays, and the vertex is where they join.
Protractor
- A protractor is used to measure angles in degrees (°).
Parallel Lines
- Parallel lines never intersect no matter how much they are extended.
- They are denoted by ||, for example, c || d.
Perpendicular Lines
- Perpendicular lines intersect at a right angle.
- They are denoted by ⊥, for example, b ⊥ c.
Transversal Line
- A transversal line cuts through two or more other lines at distinct points.
- Example: lines a and b are transversal lines.
Types of Angles Formed by a Transversal and Parallel Lines
- Interior Angles: Angles inside the two parallel lines, e.g., ∠23, ∠25, ∠26, ∠27, ∠28, ∠29, ∠10.
- Exterior Angles: Angles outside the two parallel lines, e.g., ∠21, ∠22, ∠24, ∠11, ∠12, ∠13, ∠14.
Types of Angles
- Adjacent Angles: Angles sharing one vertex and one side, e.g., ∠10 & ∠14, ∠25 & ∠26.
- Alternate Interior Angles: Interior angles on opposite sides of the transversal line, e.g., ∠26 & ∠29, ∠3 & ∠8.
- Alternate Exterior Angles: Exterior angles on opposite sides of the transversal line, e.g., ∠21 & ∠14, ∠24 & ∠11.
- Same-side Interior Angles: Interior angles on the same side of the transversal line, e.g., ∠23 & ∠27, ∠26 & ∠10.
- Same-side Exterior Angles: Exterior angles on the same side of the transversal line, e.g., ∠24 & ∠12, ∠21 & ∠13.
- Corresponding Angles: Non-adjacent interior and exterior angles on the same side of the transversal, e.g., ∠26 & ∠14, ∠24 & ∠8.
- Complementary Angles: Two angles adding up to 90°, forming a right angle, e.g., ∠22 & ∠24, ∠2 & ∠11.
- Supplementary Angles: Two angles adding up to 180°, forming a straight angle, e.g., ∠11 & ∠12, ∠1 & ∠14.
Congruent Triangles: SSS and SAS
- SSS (Side, Side, Side): If all three sides of one triangle are equal to the corresponding sides of another triangle, the triangles are congruent.
- SAS (Side, Angle, Side): If two sides and the included angle of one triangle are equal to the corresponding parts of another triangle, the triangles are congruent.
Congruent Triangles: ASA and AAS
- ASA (Angle, Side, Angle): If two angles and the included side of one triangle are equal to the corresponding parts of another triangle, the triangles are congruent.
- AAS (Angle, Angle, Side): If two angles and the non-included side of one triangle are equal to the corresponding parts of another triangle, the triangles are congruent.
Congruent Triangles: HL
- HL (Hypotenuse, Leg): If the hypotenuse and one leg of a right triangle are equal to the corresponding parts of another right triangle, the triangles are congruent.
Congruence of Triangles
- Two figures are congruent if they have the same size and shape.
- When triangles ∆ABC ≅ ∆XYZ, the order of the letters is important.
- This indicates that corresponding angles and sides are congruent: ∠A ≅ ∠X, ∠B ≅ ∠Y, ∠C ≅ ∠Z, AB ≅ XY, BC ≅ YZ, AC ≅ XZ.
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