Geometry Chapter 13

Question 1

The largest angle of a triangle is opposite

Answer 1

the longest side.

Question 1

The perpendicular from a point to a line

Answer 1

is the shortest segment from the point to the line.

Question 2

If unequals are multiplied by the same negative number

Answer 2

the results are unequal in the opposite order.

Question 2

If unequals are divided by the same negative number

Answer 2

the results are unequal in the opposite order.

Question 2

The sum of the lengths of two sides of a triangle

Answer 2

is greater than the length of the third side.

Question 2

If two sides of a triangle are congruent to two sides of another triangle

Answer 2

the triangle having the greater included angle has the greater third side.

Question 2

In the same or equal circles, the greater arc has

Answer 2

the greater central angle.

Question 4

The whole is greater than

Answer 4

any of its parts

Question 4

The length of a line segment is the

Answer 4

shortest distance between two points

Question 5

The length of the longest side of a triangle

Answer 5

is less than the sum of the lengths of the other two sides and greater than their difference.

Question 7

If unequals are added to unequals of the same order

Answer 7

the sums are unequal in the same order

Since 5>3 and 4>1, we have 5+4>3+1 (or 9>4). If 2x-4

Question 8

If the measures of two angles of a triangle are unequal

Answer 8

the lengths of the sides opposite these angles are unequal, the longer side being opposite the larger angle.

Question 9

If the lengths of two sides of a triangle are unequal

Answer 9

the measures of the angles opposite these sides are unequal, the larger angle being opposite the longer side.

Question 10

If two sides of a triangle are congruent to two sides of another triangle

Answer 10

the triangle having the greater third side has the greater angle opposite this side.

Question 11

In the same or equal circles, the greater chord

Answer 11

has the greater minor arc

Question 13

If unequals are subtracted from equals,

Answer 13

the differences are unequal in the opposite order.

Since 10=10 and 5>3, we have 10-5<10-3 (or 5<7). If x+y=12 and y>5, then x+y-y<12-5 or x<7.

Question 14

In the same or equal circles, the greater central angle

Answer 14

has the greater arc.

Question 15

In the same or equal circles, the chord at the smaller distance from the center

Answer 15

is the greater chord.

Question 17

If equals are added to unequals

Answer 17

the sums are unequal in the same order

since 5>4 and 4=4, we know that 5+4>4+4 (or 9>8). If x-4+4

Question 19

A quantity may be substituted for its equal

Answer 19

in any inequality.

If x>y and y=10, then x>10

Question 20

The longest side of a triangle is opposite

Answer 20

the largest angle.

Question 21

In a triangle, the measure of an exterior angle is

Answer 21

larger than the measure of either nonadjacent interior angle.

Question 22

If equals are subtracted from unequals

Answer 22

the differences are unequal in the same order

Since 10>5 and 3=3, we have 10-3>5-3 (or 7>2). If x+6

Question 23

If unequals are divided by the same positive number

Answer 23

the results are unequal in the same order.

Question 24

In the same or equal circles, the greater chord is

Answer 24

at a smaller distance from the center.

Question 25

If unequals are multiplied by the same positive number

Answer 25

the products are unequal in the same order.

Question 27

If the first of three quantities is greater than the second and the second is greater than the third

Answer 27

then the first is greater than the third.

If x>y and y>z, then x>z

Question 28

In the same or equal circles, the greater minor arc has

Answer 28

the greater chord