M2T1L3-4

​M2T1L3-4

Huetson - ​Geometry Honors

Multiple Choice

Which of the following represents a central angle?

Multiple Choice

What is does x equal?

• $$160\degree$$

• $$80\degree$$

• $$40\degree$$

• $$360\degree$$

Multiple Choice

inscribed angle: an angle with its vertex _____________ the circle

• at the center of
• on

Multiple Choice

The inscribed angle is ____ the measure of the intercepted arc.

• congruent to

• half
• double
• supplementary to 

Multiple Choice

An inscribed angle that intercepts a semicircle   measures  is a(n) ___________ angle.

• right
• acute
• obtuse

Multiple Choice

Find the measure of arc AB.

• 17
• 34
• 68
• 146

Multiple Choice

8.

• 67.5°
• 90°
• 22.5°
• 45°

​Conditionals vs Converse

The converse of an if-then statement is the statement that results from interchanging the hypothesis (the “if” part) and the conclusion (the “then” part) of the original statement.

​Biconditional Statement

When a conditional statement and its converse are both true, this is called a biconditional statement. A biconditional statement is a statement written in the form “if and only if p, then q.” It is a combination of both a conditional statement and the converse of that conditional statement.

Multiple Choice

Which of the following is true about the conditional statement below?

If you are in Alaska, then you are

cold.

• Hypothesis: you are in Alaska

  Conclusion: you are

  cold

• Hypothesis: IF you are in Alaska

  Conclusion: THEN you are

  cold

• Hypothesis: THEN you are

  cold

  Conclusion: IF you are in Alaska

• Hypothesis: you are

  cold

  Conclusion: you are in Alaska

Multiple Choice

Which of the following is true about the conditional statement below?

If you are flying, then you are in a

jet.

• Hypothesis: you are flying

  Conclusion: you are in a

  jet

• Hypothesis: IF you are flying

  Conclusion: THEN you are in a

  jet

• Hypothesis: THEN you are in a

  jet

  Conclusion: IF you are flying

• Hypothesis: you are in a

  jet

  Conclusion: you are flying

Multiple Choice

Which of the following is the CONVERSE of the statement below?

If an object is a ring, then it is

made of gold.

• If an object is made of gold, then it is a ring.

• If an object is not a ring, then it is not made of god.

• If an object is not made of gold, then it is not a ring.

• There is no converse of the statement.

Multiple Choice

Which of the following is the CONVERSE of the statement below?

If an object is a bird, then it can fly.

• If an object can fly, then it is a bird.

• If an object is not a bird, then it cannot fly

• If an object cannot fly, then it is not a bird

• There is no converse of the statement

Multiple Choice

Which of the following is a valid conditional statement for the following phrase:

An acute angle has a measure less than 90°.

• If an angle is acute, then it has a measure less than 90°.

• If an angle is not acute, then it does not have a measure less than 90°.

• If an angle is acute, then it is acute.

• If an angle does not measure less than 90°, then it is not acute.

Multiple Choice

If the conditional statement was "If an angle is acute, then it has a measure less than 90°.", which type of statement is the following?

An angle is acute if and only if (iff) it has a measure less than 90°.

• Biconditional

• Converse

• Inverse

• Contrapositive

Multiple Choice

If the conditional statement was "If an angle is acute, then it has a measure less than 90°.", which type of statement is the following?

If an angle has a measure less than 90°, then it is acute.

• Converse

• Contrapositive

• Biconditional

• Inverse

Multiple Choice

Write a definition of congruent angles as a biconditional statement.

• Angles are congruent if they have the same size and shape.

• If angles are congruent, then they have the same size and shape.

• Congruent angles are the same.

• Angles are congruent if and only if they have the same size and shape.

Multiple Select

Select the conditional statement(s) of the biconditional statement.

Points are collinear if and only if they all lie in one line.

• If collinear points lie in one line, then they are a line.

• If points all lie in one line, then they are collinear.

• Collinear points lie in one line.

• If points are collinear, then they all lie in one line.

Multiple Choice

When can a biconditional statement be true?

• When the inverse and the converse are both true
• When the original statement (conditional statement) & the contrapositive are both true.
• When the converse is true.
• When the original statement (conditional statement) and the converse are both true.

Multiple Choice

Determine if the statement will have a biconditional that is true or false. Then write the converse.

If Juan lives in Waukegan, then he lives in Illinois.

• True; If Juan lives in Waukegan, then he lives in Illinois.

• True; If Juan lives in Illinois, then he lives in Waukegan.

• False; If Juan lives in Waukegan, then he lives in Illinois.

• False; If Juan lives in Illinois, then he lives in Waukegan.

Multiple Choice

Which conditional statement has a false biconditional?

• If all 3 sides of a triangle are congruent, then it is an equilateral triangle.

• If all sides of a polygon are congruent,

  then it is a regular polygon.

• If all sides of quadrilateral are congruent, then it is a square.

• If a quadrilateral has only one pair of opposite congruent sides, then it is an isosceles trapezoid.

Multiple Choice

Which Conditional Statement has a false Biconditional?

• If two angles are vertical, then they are congruent.

• If two angles have the same measure, then they are congruent.

• If a polygon has only four sides, then the polygon is a quadrilateral.

• If two lines do not intersect, then they are parallel.

Replace this with your body text.

​Duplicate this text as many times as you would like.

​

​Can you solve problems using this vocabulary?

​Bisecting an Angle

​

​Angle Bisector Theorem

Multiple Choice

Name the dashed segment:

• altitude
• angle bisector
• perpendicular bisector
• median

Multiple Choice

A ray that divides an angle into two congruent angles is called .............

• perpendicular bisector

• angle bisector

• vertex

• divider

Multiple Choice

Angle JHG measures 161.

• m∠GHK=80.5,

  m∠KHJ=161

• m∠GHK=161,

  m∠KHJ=80.5

• m∠GHK=80.5,

  m∠KHJ=80.5

• m∠GHK=161,

  m∠KHJ=161

Multiple Choice

If $$\overrightarrow{KM}$$  bisects  $$\angle LKJ$$  and  $$m\angle JKM=22\degree$$  find  $$m\angle LKM$$  .

• 22

• 44

• 11

• 68

• not enough information given

Multiple Choice

If $$\overrightarrow{KM}$$  bisects  $$\angle LKJ$$  and  $$m\angle JKM=22\degree$$  find  $$m\angle LKJ$$  .

• 22

• 44

• 11

• 68

• not enough information given

Multiple Choice

• x=3/17
• x=9
• x=3
• x= -3

Multiple Choice

Solve for x.

• 2

• 3

• 4

• 5

• 7.4

Multiple Choice

If line segment BD is the angle bisector of angle ABC, line segment BE is the angle bisector of angle ABD, and the measurement of angle DBC= 24 degrees, what is the measurement of angle EBC?

• 12 degrees

• 24 degrees

• 36 degrees

• 48 degrees

​Can you solve problems using this vocabulary?

​Perpendicular Bisector Theorem

Multiple Choice

Fill in the blank:

A perpendicular bisector is perpendicular to and passing through the ___________________ of a segment.

• endpoint

• corner

• midpoint

• side

Multiple Choice

Perpendicular bisector which divides a line segment into

• Two equal parts

• single part

• Three parts

• None of the above

Multiple Choice

Identify the perpendicular bisector.

• $$\overline{TP}$$

• $$\overline{RS}$$

• $$\overline{TR}$$

• $$\overline{ST}$$

Multiple Choice

Fill in the blank:

A point that is the same distance from two figures is ___________________ from from the two figures.

• Equidistant

• Congruent

• Vertical

• Corresponding

Multiple Choice

Find BC.

• BC = 4

• BC = 16

• BC = 12

• BC = 24

Multiple Choice

• JM = 5

• JM = 10

• JM = 12

• JM = 24

Multiple Choice

Solve for the value of x.

• x = 10

• x = 20

• x = 3

• x = 45

Multiple Choice

• QR = 4

• QR = 20

• QR = 11

• QR = 5

Multiple Choice

Solve for x

• 7

• 3

• 10

• 6

Multiple Choice

What is the length of DC

• 4
• 1
• 2
• 3

​Can you solve problems using this vocabulary?

​Triangle Angle Sum Theorem

Multiple Choice

What do the interior angles in a triangle have a sum of?

• 180
• 90
• 360
• 270

Multiple Choice

Find the measure of the indicated angle. 

• 95
• 85
• 35
• 45

Multiple Choice

What is the value of the missing angle?

• 61
• 50
• 60
• 69

Multiple Choice

What is the measure of angle b

• 146
• 34
• 36
• 136

Multiple Choice

Find the measure of the indicated angle. 

• 34
• 46
• 62
• 36

​Can you solve problems using this vocabulary?

​Triangle Exterior Angle Theorem

Multiple Choice

Which of the following terms best describes Angle d?

• Remote interior angle
• Corresponding angle
• Exterior angle
• Interior angle

Multiple Choice

Which of the following angles are remote interior angles to angle d?

• Angle a and Angle b
• Angle b and Angle c
• Angle a and Angle c
• Angle a and Angle b and Angle c

Multiple Choice

What is the measure of angle b?

• 36^o
• 56^o
• 63^o
• 117^o

Multiple Choice

Find the measure of angle x.

• 138
• 96
• 93
• 87

Multiple Choice

Find the measure of each angle indicated.

• 48
• 87
• 35
• 40

Multiple Choice

Solve for x.

• 6
• 8
• 15
• 13

Multiple Choice

Solve for x. 

• A
• B
• C
• D