Geometry exam

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Questions and Answers

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?

SAS (correct)

AAS

ASA

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?

Two angles and a side that is not included are congruent. Signup and view all the answers

Which congruence criterion does NOT require a side to be included between two angles?

AAS Signup and view all the answers

What type of angles are ∠10 and ∠14 if they share a common vertex and side?

Adjacent Angles Signup and view all the answers

Which angles are considered alternate interior angles?

∠26 and ∠29 Signup and view all the answers

If two angles sum up to 180°, what type of angles are they?

Supplementary Angles Signup and view all the answers

What are same-side exterior angles?

Angles lying on the same side of the transversal Signup and view all the answers

Which of the following angles are complementary?

∠22 and ∠24 Signup and view all the answers

What defines two triangles as being congruent?

They have the same size and shape with corresponding sides and angles congruent. Signup and view all the answers

If triangle ABC is congruent to triangle PQR, what is true about the angles?

∠A is congruent to ∠P. Signup and view all the answers

Which of the following statements about corresponding parts of congruent triangles is true?

Corresponding sides and angles must be congruent. Signup and view all the answers

How should the triangles be labeled to show congruence properly?

The matching vertices must pair consistently across both triangles. Signup and view all the answers

What can be concluded if ∆ABC ≅ ∆XYZ?

AB ≅ YZ, BC ≅ XY, AC ≅ XZ. Signup and view all the answers

What defines two lines as parallel?

They do not intersect regardless of extension. Signup and view all the answers

Which of the following terms describes a line that intersects two or more lines at different points?

Transversal line Signup and view all the answers

Which angles are located inside two parallel lines?

Interior angles Signup and view all the answers

How are perpendicular lines represented?

By the symbol ⊥ Signup and view all the answers

What is the common term for angles that are opposite each other when two lines intersect?

Vertical angles Signup and view all the answers

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.