Chapter 5 Geometry

Brad places a mirror on the ground 10 ft. away from the base of a bush at a botanical garden. He walks back towards the bush until he can see the top of the bush in the mirror. If Brad is standing 4 ft. away from the mirror, and is 6 ft. tall, how tall is the bush?

15 ft. - Applications of Similar Triangles

In the pictured triangle, FE is an angle bisector. What is the length of GE?

16 - Angle Bisector Theorem: Proof and Example

In the pictured triangle, XV is an angle bisector. What is the length of XY?

24- Angle Bisector Theorem: Proof and Example

In the pictured triangle, AD is an angle bisector. What is the length of AC?

27 - Angle Bisector Theorem: Proof and Example

Two triangles are similar. The smaller triangle has angles that measure 30, 60, and 90. The larger triangle has two angles that measure 60 and 90. What must the third angle measure?

30 - Similarity Transformations in Corresponding Figures

Greg is standing next to a 40 ft. tree. The sun casts a 5 ft. shadow of Greg, who is 6.4 ft. tall. How long is the tree's shadow?

31.25 ft. - Applications of Similar Triangles

The two triangles shown below are similar. Find the length of the side labeled x.

39- Practice Proving Relationships using Congruence & Similarity

Triangle HYV and triangle AYB are similar by the AA similarity theorem. What is the value of x?

40.375 - Applications of Similar Triangles

Study the given diagram. Find the value of x, the distance between T and E.

5.625 - Applications of Similar Triangles

In the pictured triangle, MS is an angle bisector. What is the length of SO?

6 - Angle Bisector Theorem: Proof and Example

Find the measure of MN:

7 - Perpendicular Bisector Theorem: Proof and Example

Two rectangles are similar. The smaller rectangle has a bottom side length of 3 and the larger rectangle has the corresponding side length of 30. If the left side length of the smaller rectangle is 7, what is the measure of the corresponding left side of the larger rectangle?

70 - Similarity Transformations in Corresponding Figures

The triangles shown below are similar. Find the length of the side labeled x.

8 - Practice Proving Relationships using Congruence & Similarity

Given triangles DAR and KMR. What is the value of y?

9.625 - Applications of Similar Triangles

What additional information do you need to prove that triangle ABC is congruent to triangle DEF using the HA theorem?

A=D - The HA (Hypotenuse Angle) Theorem: Proof, Explanation, & Examples

If triangle ACB is congruent to triangle YXZ, all of the following are true EXCEPT:

A=Z - The HL (Hypotenuse Leg) Theorem: Definition, Proof, & Examples

Which theorem or postulate can be used to establish congruence with the pictured triangles?

AAS - The AAS (Angle-Angle-Side) Theorem: Proof and Examples

Which statement about the pictured triangle must be true?

AB=AC - Congruency of Isosceles Triangles: Proving the Theorem

If triangle ABC is congruent to triangle ADC, what must also be true?

AB=AD - The HA (Hypotenuse Angle) Theorem: Proof, Explanation, & Examples

What additional information do you need to prove that triangle ACD is congruent to triangle DBA using the HL theorem?

AB=CD - The HL (Hypotenuse Leg) Theorem: Definition, Proof, & Examples

What additional information do you need to prove that triangle ABC is congruent to triangle DEF using the HL theorem?

AC=DF - The HL (Hypotenuse Leg) Theorem: Definition, Proof, & Examples

If the pictured triangles are congruent, what reason can be given?

ASA postulate - Triangle Congruence Postulates: SAS, ASA & SSS

Which of the following statements is true regarding congruence and similarity?

All of these statements are true - How to Prove Relationships in Figures using Congruence & Similarity

Which of these relationships can NOT be used to prove that two triangles are congruent?

Angle Angle Angle - The angle measurements of each triangle are equal - Practice Proving Relationships using Congruence & Similarity

What additional information do you need to be given to prove that triangle PQS is congruent to triangle SRP using the HA theorem?

Angles PQS and SRP are right angles - The HA (Hypotenuse Angle) Theorem: Proof, Explanation, & Examples

All of the following statements about the pictured triangle must be true, EXCEPT:

BAC=ACB - Congruency of Isosceles Triangles: Proving the Theorem

In an isosceles triangle, which of the following are congruent?

Base angles and legs - Congruency of Isosceles Triangles: Proving the Theorem

The hypothesis of a conditional statement:

Begins with 'if' and comes first. - Converse of a Statement: Explanation and Example

The conclusion of a conditional statement:

Begins with 'then' and comes second. - Converse of a Statement: Explanation and Example

Triangle ABC is congruent to triangle XYZ. What reason can we use to explain why angle A is congruent to angle X?

CPCTC - Congruence Proofs: Corresponding Parts of Congruent Triangles

The converse of a conditional statement:

Can be true or false. - Converse of a Statement: Explanation and Example

Find the measure of XZ:

Cannot be determined - Perpendicular Bisector Theorem: Proof and Example

Which theorem or postulate can be used to establish congruence with the pictured triangles?

Congruence cannot be determined - The AAS (Angle-Angle-Side) Theorem: Proof and Examples

Which theorem can be used to establish congruence with the pictured triangles?

Congruence cannot be determined - Congruency of Right Triangles: Definition of LA and LL Theorems

What kind of triangles have the same size AND shape?

Congruent - Practice Proving Relationships using Congruence & Similarity

The perpendicular bisector theorem states that if a point is on the perpendicular bisector of a segment, then it is:

Equidistant from the segment's endpoints. - Perpendicular Bisector Theorem: Proof and Example

If two sides of a triangle are congruent, then which of the following statements MUST be true?

Explanation: The only statement that must be true is that the angles opposite the congruent sides are congruent. While the triangle is isosceles, it may also be equilateral or right, but not necessarily. - Congruency of Isosceles Triangles: Proving the Theorem

Which theorem can be used to establish congruence with the pictured triangles?

HA theorem - Congruency of Right Triangles: Definition of LA and LL Theorems

Which theorem can be used to establish congruence with the pictured triangles?

HL theorem - Congruency of Right Triangles: Definition of LA and LL Theorems

The converse of the perpendicular bisector theorem states that:

If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment. - Perpendicular Bisector Theorem: Proof and Example

Which theorem can be used to establish congruence with the pictured triangles?

LA theorem - Congruency of Right Triangles: Definition of LA and LL Theorems

Which theorem can be used to establish congruence with the pictured triangles?

LL theorem - Congruency of Right Triangles: Definition of LA and LL Theorems

If triangle MNO is congruent to triangle STR, what must also be true?

M=S - The HL (Hypotenuse Leg) Theorem: Definition, Proof, & Examples

If triangle ABC is congruent to triangle RST, all of the following are true EXCEPT:

NOT AB=RS - The HA (Hypotenuse Angle) Theorem: Proof, Explanation, & Examples

If triangle ABD is congruent to triangle CDB, CPCTC explains which of the following statements?

NOT ADB=DCB - Congruence Proofs: Corresponding Parts of Congruent Triangles

If the pictured triangles are congruent, what reason can be given?

NOT ASA postulate - Triangle Congruence Postulates: SAS, ASA & SSS

AD is a perpendicular bisector. Find the measure of AC:

NOT Cannot be determined - Perpendicular Bisector Theorem: Proof and Example

If triangle MNO is congruent to triangle PQR, CPCTC explains which of the following statements?

O=R - Congruence Proofs: Corresponding Parts of Congruent Triangles

Which of the following represents the angle bisector theorem for the pictured triangle?

QR/RT = QS/ST - Angle Bisector Theorem: Proof and Example

Which of the following are similar figures?

Rectangle A measures 1 x 2. Rectangle B measures 6 x 12. - Similarity Transformations in Corresponding Figures

The converse of a conditional statement:

Reverses the hypothesis and conclusion. - Converse of a Statement: Explanation and Example

The hypotenuse angle theorem is only applicable with which of the following types of triangles?

Right triangles - The HA (Hypotenuse Angle) Theorem: Proof, Explanation, & Examples

The hypotenuse leg theorem is only applicable with which of the following types of triangles?

Right triangles - The HL (Hypotenuse Leg) Theorem: Definition, Proof, & Examples

Which theorem or postulate can be used to establish congruence with the pictured triangles?

SAS - The AAS (Angle-Angle-Side) Theorem: Proof and Examples

If the pictured triangles are congruent, what reason can be given?

SAS postulate - Triangle Congruence Postulates: SAS, ASA & SSS

Which theorem or postulate can be used to establish congruence with the pictured triangles?

SSS - The AAS (Angle-Angle-Side) Theorem: Proof and Examples

How can we explain that the pictured triangles are congruent?

SSS postulate - Congruence Proofs: Corresponding Parts of Congruent Triangles

If the pictured triangles are congruent, what reason can be given?

SSS postulate - Triangle Congruence Postulates: SAS, ASA & SSS

What kind of triangles have the same shape but different sizes?

Similar - Practice Proving Relationships using Congruence & Similarity

Which of the following is a property of two similar figures?

The sides of the figures are proportional. - How to Prove Relationships in Figures using Congruence & Similarity

If two angles of a triangle are congruent, then which of the following statements must be true?

The sides opposite the congruent angles are congruent AND the triangle is isosceles. - Congruency of Isosceles Triangles: Proving the Theorem

If the pictured triangles are congruent, what reason can be given?

The triangles are not necessarily congruent - Triangle Congruence Postulates: SAS, ASA & SSS

Which of the following is a property of congruent figures?

Their corresponding angles have equal measure. - How to Prove Relationships in Figures using Congruence & Similarity

The AAS theorem requires which of the following to be congruent?

Two angles and any side - The AAS (Angle-Angle-Side) Theorem: Proof and Examples

In the pictured triangles, what reason can we use to explain that angle QPR is congruent to angle SPT?

Vertical angles - Congruence Proofs: Corresponding Parts of Congruent Triangles

Suppose the square ABCD is congruent to square EFGH. What property of congruent figures can we use to prove that the area of EFGH is 16ft.2?

We use the property that corresponding sides of congruent figures have equal length. - How to Prove Relationships in Figures using Congruence & Similarity

Assume ΔABC is similar to ΔDEF, and we want to use the properties of similar figures to prove that ∠D + ∠F = 90°. Which property do we use and how?

We use the property that the corresponding angles of similar figures are equal to show that ∠D + ∠F = ∠A + ∠C, then we plug in measures for angles A, B, and C, showing that ∠D + ∠F = 90. - How to Prove Relationships in Figures using Congruence & Similarity

All of the following are conditional statements EXCEPT:

When it's foggy, then you should use your headlights. - Converse of a Statement: Explanation and Example

For two figures to be similar, what must all the corresponding angles be?

congruent - Similarity Transformations in Corresponding Figures

For two figures to be similar, what must the corresponding sides be?

proportional - Similarity Transformations in Corresponding Figures