L N = 24 LN=24 L N = 2 4 , O M = 9 y − 43 OM=9y-43 O M = 9 y − 4 3 , and O M ‾ \overline{OM} O M is a perpendicular bisector of L N ‾ \overline{LN} L N . Determine which of the following is true.

perimeter of Δ L M N = 74 \Delta LMN\ =\ 74 Δ L M N = 7 4

perimeter of Δ M O N \Delta MON Δ M O N = 69

X is a midpoint of \overline{UV} U V and Y is a midpoint of U W ‾ \overline{UW} U W .

V W ‾ ∥ X Y ‾ \overline{VW}\ \parallel\ \overline{XY} V W ∥ X Y

\overline{VX}\ \cong\ \overline{XU} V X ≅ X U

V X ‾ ≅ Y W ‾ \overline{VX}\ \cong\ \overline{YW} V X ≅ Y W

X U ‾ ≅ U Y ‾ \overline{XU}\ \cong\ \overline{UY} X U ≅ U Y

V W ‾ ≅ 1 2 X Y ‾ \overline{VW}\ \cong\ \frac{1}{2}\overline{XY} V W ≅ 2 1 X Y

In Δ A B C \Delta ABC Δ A B C AB = 12 BC = 24 CA = 30 What order are the angles listed in order from smallest to largest?

∠ C , ∠ A , ∠ B \angle C,\ \angle A,\ \angle B ∠ C , ∠ A , ∠ B

∠ A , ∠ B , ∠ C \angle A,\ \angle B,\ \angle C ∠ A , ∠ B , ∠ C

∠ B , ∠ C , ∠ A \angle B,\ \angle C,\ \angle A ∠ B , ∠ C , ∠ A

∠ C , ∠ B , ∠ A \angle C,\ \angle B,\ \angle A ∠ C , ∠ B , ∠ A

Not enough information. An equiangular triangle is not necessarily equilateral.

Which of the following relationships are true. Select all that apply.

A C ‾ ∥ D E ‾ \overline{AC}\ \parallel\ \overline{DE} A C ∥ D E

m ∠ B A C = 2 ( m ∠ B C A ) m\angle BAC\ =\ 2\left(m\angle BCA\right) m ∠ B A C = 2 ( m ∠ B C A )

m ∠ B D E = m ∠ B E D m\angle BDE=m\angle BED m ∠ B D E = m ∠ B E D

What additional information makes it possible to prove \Delta ABC Δ A B C is an isosceles triangle?

A M ‾ ≅ C P ‾ \overline{AM}\ \cong\ \overline{CP} A M ≅ C P

B M ‾ ≅ B P ‾ \overline{BM}\ \cong\ \overline{BP} B M ≅ B P

∠ M A N ≅ ∠ Q P C \angle MAN\ \cong\ \angle QPC ∠ M A N ≅ ∠ Q P C

Δ M A N \Delta MAN Δ M A N is an isosceles triangle.

Given: Δ A B C \Delta ABC Δ A B C with B C > A C . BC\ >\ AC. B C > A C . Prove: m ∠ A ≠ m ∠ B m\angle A\ \ne\ m\angle B m ∠ A  = m ∠ B Which of the following could be a statement in the indirect proof ?

By the converse of the isosceles base angles theorem, B C = A C . BC\ =\ AC. B C = A C .

By the definition of base angles of an isosceles triangle, ∠ A ≅ ∠ B \angle A\ \cong\angle B ∠ A ≅ ∠ B

By the definition of base angles of an isosceles triangle, ∠ B ≅ ∠ C . \angle B\cong\angle C. ∠ B ≅ ∠ C .

By the converse of the hinge theorem, m ∠ A > m ∠ B m\angle A>m\angle B m ∠ A > m ∠ B

Relationships Within Triangles

Authored by Jennifer Molina

Mathematics

9th - 12th Grade

CCSS covered

Used 51+ times

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20 questions

Show all answers

MULTIPLE SELECT QUESTION

15 mins • 1 pt

Which of the following measures can be side lengths of a triangle?

10, 12, 15

3, 9, 12

6, 6, 13

5, 7, 9

Tags

CCSS.7.G.A.2

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Given $AM=BM$ and $AC=BC$ , what is $m\angle MBC$ ?

Tags

CCSS.HSG.CO.C.9

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Solve for y.

Tags

CCSS.8.G.A.5

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

In the isosceles triangle $QRS$ , $\overline{RT}$ is the angle bisector of $\angle QRS$ . You want to prove the base angles of this triangle are congruent. You start by stating $\angle1\cong\angle2$ . What is a valid reason for this statement?

Reflexive property of congruence

Definition of angle bisector

Symmetric property of congruence

Corresponding angles are congruent

Tags

CCSS.HSG.CO.C.9

MULTIPLE SELECT QUESTION

15 mins • 1 pt

Which of the following measures can be side lengths of a triangle?

9, 1, 4

6, 3, 5

21, 20, 2

7, 14, 7

Tags

CCSS.7.G.A.2

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

What is $m\angle B$ ?

180

140

Tags

CCSS.8.G.A.5

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

What is y?

110

Tags

CCSS.8.G.A.5

MULTIPLE SELECT QUESTION

15 mins • 1 pt

$LN=24$ , $OM=9y-43$ , and $\overline{OM}$ is a perpendicular bisector of $\overline{LN}$ .
Determine which of the following is true.

y = 8

LM = 12

OM = 20

perimeter of $\Delta MON$ = 69

perimeter of $\Delta LMN\ =\ 74$

Tags

CCSS.HSG.CO.C.9

10.

MULTIPLE SELECT QUESTION

15 mins • 1 pt

X is a midpoint of $\overline{UV}$ and Y is a midpoint of $\overline{UW}$ .

$\overline{VX}\ \cong\ \overline{YW}$

$\overline{XU}\ \cong\ \overline{UY}$

$\overline{VW}\ \cong\ \frac{1}{2}\overline{XY}$

$\overline{VW}\ \parallel\ \overline{XY}$

$\overline{VX}\ \cong\ \overline{XU}$

Tags

CCSS.HSG.SRT.B.4

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Relationships Within Triangles

Which of the following measures can be side lengths of a triangle?

Given AM=BMAM=BMAM=BM and AC=BCAC=BCAC=BC , what is m∠MBCm\angle MBCm∠MBC ?

Solve for y.

In the isosceles triangle QRSQRSQRS , RT‾\overline{RT}RT is the angle bisector of ∠QRS\angle QRS∠QRS . You want to prove the base angles of this triangle are congruent. You start by stating ∠1≅∠2\angle1\cong\angle2∠1≅∠2 . What is a valid reason for this statement?

Which of the following measures can be side lengths of a triangle?

What is m\angle Bm∠B ?

What is y?

What is x?

LN=24LN=24LN=24 , OM=9y−43OM=9y-43OM=9y−43 , and OM‾\overline{OM}OM is a perpendicular bisector of LN‾\overline{LN}LN .Determine which of the following is true.

X is a midpoint of \overline{UV}UV and Y is a midpoint of UW‾\overline{UW}UW .

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Given $AM=BM$ and $AC=BC$ , what is $m\angle MBC$ ?

In the isosceles triangle $QRS$ , $\overline{RT}$ is the angle bisector of $\angle QRS$ . You want to prove the base angles of this triangle are congruent. You start by stating $\angle1\cong\angle2$ . What is a valid reason for this statement?

What is $m\angle B$ ?

$LN=24$ , $OM=9y-43$ , and $\overline{OM}$ is a perpendicular bisector of $\overline{LN}$ .
Determine which of the following is true.

X is a midpoint of $\overline{UV}$ and Y is a midpoint of $\overline{UW}$ .