AnswersGeometry - Semester 1 PathwaysIsosceles Triangles

Isosceles Triangles — Cumulative exam Answers

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Given: HF || JK; HG ≅ JGProve: FHG ≅ KJG

Question illustration
A
FGH ≅ KGJ because vertical angles are congruent.
Option A
B
JKG ≅ HFG because vertical angles are congruent.
Option B
C
FHG ≅ JKG because right angles are congruent.
Option C
D
HFG ≅ KJG because alternate interior angles are congruent.
Option D
2
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The proof that ΔRST ≅ ΔVST is shown.Given: ST is the perpendicular bisector of RV.Prove: ΔRST ≅ ΔVST

Question illustration
A
perpendicular bisector theorem
B
converse of the perpendicular bisector theorem
C
Pythagorean theorem
D
SSS congruence theorem
3

On a coordinate plane, 2 quadrilaterals are shown. The first figure has points A (negative 2, 1), B (negative 4, 1), C (negative 4, 5), and D (negative 2, 4). Figure 2 has points A prime (2, 1), B prime (4, 1), C prime (4, 5), and D prime (2, 4).

Question illustration
A
rx-axis(x, y) → (–x, y)
B
ry-axis(x, y) → (–x, y)
C
rx-axis(x, y) → (x, –y)
D
ry-axis(x, y) → (x, –y)
4

Parallelogram L M N O is shown. Angle N is (2 x) degrees and angle L is (3 x minus 20) degrees.

Question illustration
A
20°
B
30°
C
40°
D
50°
5

Given: AB = BCProve: B is the midpoint of AC.

Question illustration
A
two-column proof
B
one-paragraph proof
C
flowchart proof
D
two-paragraph proof
6

Figure ABCD is a parallelogram.

Question illustration
A
6
B
7
C
8
D
9
7

Triangles W X Z and Y Z X share common side X Z. Angles W X Z and X Z Y are right angles. The lengths of sides W X and Z Y are 21 centimeters.

Question illustration
A
Yes, they are congruent by SAS.
B
Yes, they are both right triangles.
C
No, the triangles share side XZ.
D
No, there is only one set of congruent sides.
8

Which pair of triangles can be proven congruent by SAS?

A
2 triangles with identical angle measures are shown. The second triangle is shifted to the right.
Option A
B
2 triangles are shown. They have 2 congruent sides and a congruent angle. The first triangle is rotated about a point to form the second triangle.
Option B
C
2 triangles are shown. They have 1 congruent side and 2 congruent angles. The first triangle is rotated about a shared side to form the second triangle.
Option C
D
Option
Option D
9

What mistakes did he make? Select two options.

A
He applied the reflection to the pre-image first.
B
He applied the rotation to the pre-image first.
C
He changed the size of the figure instead of just applying a rotation.
D
He used point P as the center of rotation.
E
He used an incorrect angle of rotation around point P.
10

Which defines a line segment?

A
two rays with a common endpoint
B
a piece of a line with two endpoints
C
a piece of a line with one endpoint
D
all points equidistant from a given point
11

On a coordinate plane, 2 triangles are shown. Triangle A B C has points (negative 3, negative 1), (negative 1, 2), and (negative 5, 3). Triangle R S T has points (1, 1), (3, 4), and (5, 0).

Question illustration
A
ΔRST ≅ ΔACB
B
ΔRST ≅ ΔABC
C
ΔRST ≅ ΔBCA
D
ΔRST ≅ ΔBAC
12

Line segment JL is an altitude in triangle JKM.

Question illustration
A
JKM is a right triangle because KL + LM = 15.3.
B
JKM is a right triangle because KL + LM = 18.2.
C
JKM is not a right triangle because KL + LM ≠ 15.3.
D
JKM is not a right triangle because KL + LM ≠ 18.2.
13

In the diagram, .

Question illustration
A
WV and XY
B
WV and ZY
C
∠VZW ≅ ∠YZX
D
∠VWZ ≅ ∠YXZ
14

Triangle DEF was tranformed to create triangle D'E'F'. Complete the statement about the transformation.

Question illustration
A
point D.
B
point E'.
C
point F.
D
point E.
15

On a coordinate plane, 5 trapezoids are shown. Trapezoid L M N P is in quadrant 2 and has points (negative 2, 3), (negative 2, 6), (negative 1, 6), and (negative 1, 4). Trapezoid B is reflected in quadrant 2. Trapezoid C is reflected across the y-axis. Trapezoid D is reflected into quadrant 4. Trapezoid A is reflected across the x-axis.

Question illustration
A
figure A
B
figure B
C
figure C
D
figure D
16

Triangle J K L is shown. Angle J K L is a right angle. An altitude is drawn from point K to point M on side L J to form a right angle.

Question illustration
A
ΔJKM
B
ΔMKL
C
ΔKML
D
ΔLJK
17

Triangle ABC is rotated 45° about point X, resulting in triangle EFD.

Question illustration
A
3.3 cm
B
3.6 cm
C
4.2 cm
D
4.5 cm
18

Which polynomial is in standard form?

A
mc026-1.jpg
Option A
B
mc026-2.jpg
Option B
C
mc026-3.jpg
Option C
D
mc026-4.jpg
Option D
19

Triangles A B C and D E F are shown. Triangle A B C is rotated to the left about point A and then is shifted up and to the right to form triangle D E F.

Question illustration
A
Translate vertex A to vertex D, and then reflect △ABC across the line containing AC.
B
Translate vertex B to vertex D, and then rotate △ABC around point B to align the sides and angles.
C
Translate vertex B to vertex D, and then reflect △ABC across the line containing AC.
D
Translate vertex A to vertex D, and then rotate △ABC around point A to align the sides and angles.
20

Two similar triangles are shown.

Question illustration
A
translated
B
reflected
C
dilated
D
rotated

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