Geometry Chapter 2 Review

Questions and Answers

What can be concluded about the lengths of segments created by a median in triangle PQR when PR = 16?

PS = 0 and RS = 16

PS = 16 and RS = 0

PS = 4 and RS = 12

PS = 8 and RS = 8 (correct)

What do perpendicular lines form?

Two unequal angles

Two congruent right angles (correct)

One obtuse angle

Two acute angles

What does a bisector do in terms of segment lengths?

Divides a circle into two unequal arcs

Increases the length of the segment

Divides a segment into two equal segments (correct)

Creates three unequal segments

If BD is a perpendicular bisector in triangle ABC, what can be said about segments AD and CD?

AD and CD are equal in length Signup and view all the answers

When angles formed by a bisector are considered, what can be inferred about angle CAT?

Angle CAT is congruent to angle CAB Signup and view all the answers

What is the measure of angle TAB if CAB measures 22°?

44° Signup and view all the answers

What is the conclusion about the measure of angles created by an angle bisector?

It divides the angle into two equal angles. Signup and view all the answers

If point K is the midpoint of segment TJ, which statement describes what midpoints do?

A midpoint divides a segment into two congruent segments. Signup and view all the answers

Which pair of angles represents a linear pair?

< 5 and < 6 Signup and view all the answers

What is the relationship between angles 1 and 4 if they are a linear pair?

They form a straight line together. Signup and view all the answers

If the measure of angle 1 is 40°, what can be said about the measure of angle 2?

It must be 140°. Signup and view all the answers

Which statement about angles 1 and 4 is true?

They form a linear pair. Signup and view all the answers

What is the nature of angles 5 and 9 based on provided relationships?

They are neither. Signup and view all the answers

What relationship do vertical angles have with each other?

They are congruent. Signup and view all the answers

If two angles are supplementary and one angle measures 30° more than the other, what is the measure of the larger angle?

120° Signup and view all the answers

Which of the following correctly identifies adjacent angles around a point?

They sum up to 360°. Signup and view all the answers

If the measures of two supplementary angles are 140° and x°, what is the value of x?

40° Signup and view all the answers

If one angle is 48° and it is part of a pair of supplementary angles, what is the measure of its complement?

96° Signup and view all the answers

Which angles are identified as supplementary angles?

Two angles whose measures sum to 180°. Signup and view all the answers

What is the measure of one angle if the other angles in a linear pair measure 45°?

135° Signup and view all the answers

From the angles provided in the diagram, which pair is identified as vertical angles?

two angles across from each other. Signup and view all the answers

What are three different ways to name the 47° angle in triangle DEF?

Angle EFD, ∠DEF, ∠DFE Signup and view all the answers

In a triangle, how should the smallest angle generally be denoted?

The angle opposite the smallest side Signup and view all the answers

In triangle PQR, if PR = 16 and QS is a median, what can PS be if S is the midpoint of QR?

8 Signup and view all the answers

What is the statement when BD is an altitude drawn to side AC in triangle ABC?

BD is perpendicular to AC Signup and view all the answers

What is the measure of angle ATS in trapezoid STAR if m < ATS = 48?

48 degrees Signup and view all the answers

What does it mean if BD is a perpendicular bisector in triangle ABC?

BD divides AC into two equal segments at a right angle Signup and view all the answers

If AB bisects <CAT and <CAB = 22°, what is <TAB?

22° Signup and view all the answers

Which statement explains why ST is the longest side of triangle SAT?

It is opposite the largest angle in the triangle. Signup and view all the answers

In triangle ABD, if m < A = 66 degrees, m < CDB = 18 degrees, and m < C = 24 degrees, what is the longest side of triangle ABD?

AB Signup and view all the answers

How can the largest angle in a triangle be identified?

It is always the angle opposite the longest side Signup and view all the answers

Using the Exterior Angle Theorem, what can be concluded about the angles 110 degrees and the sum of the two non-adjacent interior angles?

110 degrees equals the sum of the two interior angles. Signup and view all the answers

What is the role of point K as the midpoint of segment TJ?

K divides segment TJ into two equal parts Signup and view all the answers

If m < RAS = 68 degrees, what can be inferred about the other angles in triangle RAS?

The sum of the angles must be 180 degrees. Signup and view all the answers

What is the relationship between line RA and line ST in trapezoid STAR?

RA is parallel to ST. Signup and view all the answers

If triangle SAT has a largest angle at S, which side is necessarily the longest?

ST Signup and view all the answers

If m < C = 24 degrees, which of the following must be true about triangle ABD?

The sum of angles A and D must equal 156 degrees. Signup and view all the answers

Study Notes

Triangle Properties and Relationships

Angles in triangles can be named in multiple ways based on the symbols for each vertex.
The smallest and largest angles can be determined by comparing their measures in a triangle.
The lengths of sides in triangles correlate with the angle measures: the side opposite the largest angle is the longest side.

Altitudes and Medians

An altitude in a triangle creates a right angle with the base, indicating a perpendicular relationship.
A median divides a triangle's sides into two equal segments, meaning the median's segments are congruent.

Perpendicular Bisectors

A perpendicular bisector divides a segment into two equal parts at a right angle, creating two congruent segments.
The properties of angles formed by perpendicular lines indicate congruence.

Angle Bisectors

An angle bisector creates two equal angles within the original angle, demonstrating congruency.
If one angle's measure is given, the bisected angles can be easily calculated through division.

Midpoint and Segment Bisectors

The midpoint of a segment equally divides that segment into two congruent segments.
Midpoints serve to establish equal lengths of partitioned segments.

Angle Relationships

Vertical angles are congruent and opposite one another when two lines intersect.
Linear pairs consist of two adjacent angles that sum up to 180 degrees, implying they are supplementary.
Certain angle relationships can help determine the measures of unknown angles by using complementary or supplementary properties.

Supplementary Angles

Two angles are classified as supplementary if their measures add up to 180 degrees.
If one angle is a defined measure more than another, algebra can be used to find both angles' measures.

Algebraic Angle Solutions

Angles can be calculated using algebra when relationships or additional angles are known, such as through the properties of supplementary and vertical angles.

Diagrams and Figures

Utilizing diagrams can greatly aid in visualizing geometric relationships, making it easier to apply theorems and find solutions.

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Description

This quiz focuses on Chapter Two of Geometry, testing your understanding of triangle properties and angle notation. Answer questions about naming angles in various ways and identifying characteristics of triangles. Sharpen your geometry skills with these problems!