Geometry Hour 5-part 1

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• 1.

Which shape does not have any lines of symmetry?

• A.

A

• B.

B

• C.

C

• D.

D

D. D
Explanation
Shape D does not have any lines of symmetry.

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• 2.

• A.

35

• B.

55

• C.

110

• D.

125

B. 55
• 3.

• A.

A

• B.

B

• C.

C

• D.

D

A. A
• 4.

Which translation was used?

• A.

( x , y ) → ( x + 2, y + 3)

• B.

( x , y ) → ( x + 2, y − 3)

• C.

( x , y ) → ( x − 2, y + 3)

• D.

( x , y ) → ( x − 2, y − 3)

A. ( x , y ) → ( x + 2, y + 3)
Explanation
The correct answer is ( x , y ) → ( x + 2, y + 3). This translation involves shifting the original coordinates 2 units to the right and 3 units up.

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• 5.

Which of these reasons would be appropriate for statement 3?

• A.

Reflexive property

• B.

Definition of midpoint

• C.

Vertical angles are congruent.

• D.

Corresponding parts of congruent triangles are congruent.

C. Vertical angles are congruent.
Explanation
Vertical angles are congruent because they are formed by the intersection of two lines, creating opposite angles that have equal measures. This is a fundamental property of angles formed by intersecting lines, and it holds true regardless of the specific angles or lines involved. Therefore, it is an appropriate reason for statement 3.

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• 6.

• A.

A

• B.

B

• C.

C

• D.

D

A. A
• 7.

Which statement is true about an equilateral triangle?

• A.

It has no rotational symmetry.

• B.

It has only rotational symmetry.

• C.

It has exactly 1 line of symmetry.

• D.

It has exactly 3 lines of symmetry.

D. It has exactly 3 lines of symmetry.
Explanation
An equilateral triangle is a triangle with all three sides of equal length. Each angle in an equilateral triangle is 60 degrees. Because of its symmetry, an equilateral triangle can be rotated by 120 degrees or 240 degrees and still look the same. Therefore, it has rotational symmetry of order 3. Additionally, an equilateral triangle can be folded along three different lines to create congruent halves, meaning it has three lines of symmetry.

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• 8.

Parallelogram ABCD is shown below.

• A.

85 degrees

• B.

90 degrees

• C.

95 degrees

• D.

100 degrees

A. 85 degrees
Explanation
In a parallelogram, opposite angles are congruent. Since angle A is opposite angle C, and angle C is given as 85 degrees, angle A must also be 85 degrees.

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• 9.

Trapezoid TRAP is shown below. What is the length of the midsegment MN?

• A.

10

• B.

• C.
• D.

100

A. 10
Explanation
The length of the midsegment MN is 10. In a trapezoid, the midsegment is a line segment that connects the midpoints of the two non-parallel sides. It is parallel to the bases and its length is equal to the average of the lengths of the two bases. In this case, the length of the midsegment MN is equal to the average of the lengths of the non-parallel sides of the trapezoid, which is 10.

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• 10.

Look at the letters below How many letters have a horizontal line of symmetry?

• A.

3

• B.

5

• C.

6

• D.

8

B. 5
Explanation
There are five letters that have a horizontal line of symmetry. A horizontal line of symmetry means that when a letter is folded along a horizontal line, the two halves will match exactly. In this case, the letters that have a horizontal line of symmetry are H, I, O, X, and Z.

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• 11.

Shown below are the statements and reasons for the proof.  They are not in the correct order. Which of these is the most logical order for the statements and reasons?

• A.

I, II, III, IV, V

• B.

III, II, V, I, IV

• C.

III, II, V, IV, I

• D.

II, V, III, IV, I

B. III, II, V, I, IV
• 12.
• A.

A

• B.

B

• C.

C

• D.

D

D. D
• 13.
• A.

A′(−4, 4), B′(−3, −3), C′(−9, −1)

• B.

A′(4, −4), B′(−3, −3), C′(−1, −9)

• C.

A′(4, −4), B′(3, 3), C′(9, 1)

• D.

A′(4, 4), B′(3, −3), C′(9, −1)

C. A′(4, −4), B′(3, 3), C′(9, 1)
Explanation
The correct answer is A′(4, −4), B′(3, 3), C′(9, 1). This is because the points A', B', and C' are arranged in a way that satisfies the given coordinates. A' has coordinates (4, -4), B' has coordinates (3, 3), and C' has coordinates (9, 1). These coordinates match the given points in the question.

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• 14.
• A.

A

• B.

B

• C.

C

• D.

D

C. C
• 15.

Mr. Smith and Ms. Jones start at the same place.  Mr. Smith drives north for 4 miles.  Ms. Jones drives east for 5 miles. What is the direct distance between Mr. Smith and Ms. Jones.

• A.

miles

• B.

miles

• C.

9 miles

• D.

41 miles

B.   miles
Explanation
Since Mr. Smith drives north for 4 miles and Ms. Jones drives east for 5 miles, we can use the Pythagorean theorem to find the direct distance between them. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, the direct distance between Mr. Smith and Ms. Jones is the hypotenuse of a right triangle with legs measuring 4 miles and 5 miles. Using the Pythagorean theorem, we can calculate the square of the hypotenuse: 4^2 + 5^2 = 16 + 25 = 41. Taking the square root of 41 gives us the direct distance between Mr. Smith and Ms. Jones, which is approximately 6.4 miles.

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• 16.
• A.

A

• B.

B

• C.

C

• D.

D

D. D
• 17.
• A.

41°

• B.

65°

• C.

102°

• D.

115°

D. 115°
Explanation
The given sequence of angles is in increasing order. Each angle is larger than the previous one. The last angle in the sequence is 115°, which is the largest angle among all the given angles. Therefore, the correct answer is 115°.

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• 18.

As a classroom warm-up problem, Mrs. Hughes drew this network and asked her students to write down the path that showed traceability.

• A.

A

• B.

B

• C.

C

• D.

D

B. B
Explanation
The correct answer is B because it is the only path that connects all the nodes in the network. The path starts at A, goes to B, then to C, and finally to D, covering all the nodes in the network.

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• 19.

Look at the conditions below: 1. If a quadrilateral has 4 right angles, then it is a rectangle. 2. If a quadrilateral is a rectangle, then it could be a square. 3. Quadrilateral ABCD has 4 right angles Using these conditions, which of these is a valid conclusion?

• A.

Quadrilateral ABCD must be a square.

• B.

Quadrilateral ABCD is not a rectangle.

• C.

Quadrilateral ABCD could be a square.

• D.

Quadrilateral ABCD could be a rectangle.

C. Quadrilateral ABCD could be a square.
Explanation
The given conditions state that if a quadrilateral has 4 right angles, then it is a rectangle. It also states that if a quadrilateral is a rectangle, then it could be a square. Therefore, if a quadrilateral ABCD has 4 right angles, it could be a rectangle. Since a rectangle could be a square, it is also possible for quadrilateral ABCD to be a square. Hence, the valid conclusion is that quadrilateral ABCD could be a square.

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• 20.

• A.

(0, −12)

• B.

(0, −8)

• C.

(0, 8)

• D.

(0, 12)