Solutions Manual For Exploring Geometry 2nd Edition By
Michael Hvidsten 9781498760805 ALL CHAPTERS .
What value is a counterexample for the conditional statement shown?
If a number between 0 and 100 is an odd perfect square, then the only factors of the number are 1,
the number itself, and the square root of the number.
9
25
49
81 - ANSWER: 81
Which congruence theorems can be used to prove ΔABR ≅ ΔACR? Select three options.
HL
SAS
SSS
ASA
AAS - ANSWER: HL, SAS, SSS
△ABC is an isosceles triangle with legs AB and AC. △AYX is also an isosceles triangle with legs AY and
AX.
The proof that △ABC ~ △AYX is shown.
Statements Reasons
1. △ABC is isosceles with legs AB and AC; △AYX is also isosceles with legs AY and AX.1. given2. AB ≅
AC and AY ≅ AX2. definition of isosceles triangle3. AB = AC and AY = AX3. definition of congruency4.
AY • AC = AX • AC4. multiplication property of equality5. AY • AC = AX • AB5. substitution property of
equality6. 6. division property of equality7. 7. division property of equality8. ?8. ?9. △ABC ~ △AYX9.
SAS similarity theorem
Which statement and reason are missing in the proof?
∠A ≅ ∠A; reflexive property
∠X ≅ ∠X; reflexive property
∠ABC ≅ ∠AYX; corresponding angles of similar triangles
∠ABC ≅ ∠AXY; corresponding angles of similar triangles - ANSWER: ∠A ≅ ∠A; reflexive property
Triangle QRS is transformed as shown on the graph.
Which rule describes the transformation?
R0, 90°
R0, 180°
R0, 270°
R0, 360° - ANSWER: R0, 270°
What must be the value of x so that lines c and d are parallel lines cut by transversal p?
12
18
81
99 - ANSWER: 18
Triangle DEF is isosceles, where . Angle FDE is bisected by segment DG, creating angle GDE with a
measure of 29°.
What is the measure of angle DFE?
29°
32°
58°
64° - ANSWER: 58°
, Angles X and Y are supplementary. Angle X is 3 times the measure of angle Y. What is the measure of
angle X?
45°
60°
120°
135° - ANSWER: 135
The statements below can be used to prove that the triangles are similar.
?
△ABC ~ △XYZ by the SSS similarity theorem.
Which mathematical statement is missing?
YZ/BC = 6/3
∠B ≅ ∠Y
BC/YZ = 6/3
∠B ≅ ∠Z - ANSWER: BC/YZ = 6/3
In the diagram, mFLI is 106°, mFLG = (2x - 1)°,mGLH = (x + 17)°, and mHLI = (4x - 15)°.
What is the measure of the smallest angle in the diagram?
15°
29°
32°
45° - ANSWER: 29
What is the rule for the reflection?
rx-axis(x, y) → (-x, y)
ry-axis(x, y) → (-x, y)
rx-axis(x, y) → (x, -y)
ry-axis(x, y) → (x, -y) - ANSWER: ry-axis(x, y) → (-x, y)
Which diagram shows lines that must be parallel lines cut by a transversal?
91, 91
91, 91
89,91
91,89 - ANSWER: d. 91, 89
Angles 1 and 2 are supplementary.
Which equation represents the relationship between their measures?
m1 + m2 = 90°
m1 + m2 = 100°
m1 + m2 = 180°
m1 + m2 = 200° - ANSWER: m1 + m2 = 180°
Which composition of transformations maps figure RSTUV to figure R"S"T"U"V"?
a reflection across line n followed by a translation down and to the right
a reflection across line n followed by a 270° rotation about point P
a translation down followed by a 270° rotation about point P
a translation down followed by a reflection across line n - ANSWER: B. a reflection across line n
followed by a 270° rotation about point P
Line RS intersects triangle BCD at two points and is parallel to segment DC.
Which statements are correct? Select three options.
△BCD is similar to △BSR.
Michael Hvidsten 9781498760805 ALL CHAPTERS .
What value is a counterexample for the conditional statement shown?
If a number between 0 and 100 is an odd perfect square, then the only factors of the number are 1,
the number itself, and the square root of the number.
9
25
49
81 - ANSWER: 81
Which congruence theorems can be used to prove ΔABR ≅ ΔACR? Select three options.
HL
SAS
SSS
ASA
AAS - ANSWER: HL, SAS, SSS
△ABC is an isosceles triangle with legs AB and AC. △AYX is also an isosceles triangle with legs AY and
AX.
The proof that △ABC ~ △AYX is shown.
Statements Reasons
1. △ABC is isosceles with legs AB and AC; △AYX is also isosceles with legs AY and AX.1. given2. AB ≅
AC and AY ≅ AX2. definition of isosceles triangle3. AB = AC and AY = AX3. definition of congruency4.
AY • AC = AX • AC4. multiplication property of equality5. AY • AC = AX • AB5. substitution property of
equality6. 6. division property of equality7. 7. division property of equality8. ?8. ?9. △ABC ~ △AYX9.
SAS similarity theorem
Which statement and reason are missing in the proof?
∠A ≅ ∠A; reflexive property
∠X ≅ ∠X; reflexive property
∠ABC ≅ ∠AYX; corresponding angles of similar triangles
∠ABC ≅ ∠AXY; corresponding angles of similar triangles - ANSWER: ∠A ≅ ∠A; reflexive property
Triangle QRS is transformed as shown on the graph.
Which rule describes the transformation?
R0, 90°
R0, 180°
R0, 270°
R0, 360° - ANSWER: R0, 270°
What must be the value of x so that lines c and d are parallel lines cut by transversal p?
12
18
81
99 - ANSWER: 18
Triangle DEF is isosceles, where . Angle FDE is bisected by segment DG, creating angle GDE with a
measure of 29°.
What is the measure of angle DFE?
29°
32°
58°
64° - ANSWER: 58°
, Angles X and Y are supplementary. Angle X is 3 times the measure of angle Y. What is the measure of
angle X?
45°
60°
120°
135° - ANSWER: 135
The statements below can be used to prove that the triangles are similar.
?
△ABC ~ △XYZ by the SSS similarity theorem.
Which mathematical statement is missing?
YZ/BC = 6/3
∠B ≅ ∠Y
BC/YZ = 6/3
∠B ≅ ∠Z - ANSWER: BC/YZ = 6/3
In the diagram, mFLI is 106°, mFLG = (2x - 1)°,mGLH = (x + 17)°, and mHLI = (4x - 15)°.
What is the measure of the smallest angle in the diagram?
15°
29°
32°
45° - ANSWER: 29
What is the rule for the reflection?
rx-axis(x, y) → (-x, y)
ry-axis(x, y) → (-x, y)
rx-axis(x, y) → (x, -y)
ry-axis(x, y) → (x, -y) - ANSWER: ry-axis(x, y) → (-x, y)
Which diagram shows lines that must be parallel lines cut by a transversal?
91, 91
91, 91
89,91
91,89 - ANSWER: d. 91, 89
Angles 1 and 2 are supplementary.
Which equation represents the relationship between their measures?
m1 + m2 = 90°
m1 + m2 = 100°
m1 + m2 = 180°
m1 + m2 = 200° - ANSWER: m1 + m2 = 180°
Which composition of transformations maps figure RSTUV to figure R"S"T"U"V"?
a reflection across line n followed by a translation down and to the right
a reflection across line n followed by a 270° rotation about point P
a translation down followed by a 270° rotation about point P
a translation down followed by a reflection across line n - ANSWER: B. a reflection across line n
followed by a 270° rotation about point P
Line RS intersects triangle BCD at two points and is parallel to segment DC.
Which statements are correct? Select three options.
△BCD is similar to △BSR.
