Unit 2: Geometry

A straight angle is formed when two lines are opposite and form a straight line. In this case, the angle shown below is a straight angle because the two lines are in a straight line and are opposite each other.

The pattern in the given sequence is formed by multiplying each term by 3. Starting with 4, each subsequent term is obtained by multiplying the previous term by 3. This can be observed by multiplying 4 by 3 to get 12, then multiplying 12 by 3 to get 36, and so on. Therefore, the rule used to make the pattern is to multiply each term by 3.

The angle formed by the hands of the clock can be described as an obtuse angle. An obtuse angle is any angle that measures greater than 90 degrees but less than 180 degrees. Since the hands of the clock form an angle greater than 90 degrees, but less than a straight angle (180 degrees), it can be classified as an obtuse angle.

Option 1 appears to be a right angle because it is a 90-degree angle, which is the definition of a right angle.

The pattern in the given sequence is obtained by subtracting 50 from each number. Starting from 260, when we subtract 50, we get 210. Similarly, subtracting 50 from 210 gives us 160, and so on. Therefore, the rule used to make the pattern is to subtract 50.

Angle 3 is described as an acute angle because it measures less than 90 degrees. In the given figure, angle 3 appears to be smaller than a right angle, and it does not form a straight line. Therefore, it can be concluded that angle 3 is an acute angle.

A rectangle with four congruent sides is called a square. A square is a special type of rectangle where all four sides are equal in length. This means that all four angles of a square are also equal, measuring 90 degrees. Therefore, a square is the correct answer in this case.

The triangle shown below is an equilateral triangle because all three sides are equal in length. In an equilateral triangle, all angles are also equal, measuring 60 degrees each.

The diameter of a circle is always twice the length of its radius. Since the radius of this circle is 8 centimeters, the diameter would be 2 times 8, which equals 16 centimeters.

Angle y can be solved by using the fact that the sum of the angles in a triangle is equal to 180 degrees. Since we are given that angle y is part of a triangle and the other two angles are 13 degrees and 90 degrees, we can subtract the sum of these two angles from 180 degrees to find angle y. Therefore, angle y is equal to 180 degrees - 13 degrees - 90 degrees = 77 degrees. However, the given answer is 103 degrees, which contradicts our calculation. Therefore, the given answer is incorrect or there may be some missing information.

The given answer is 20 degrees because if we add up all the angles in a triangle, the sum should be 180 degrees. Since two angles are already given as 45 degrees and 110 degrees, the third angle can be found by subtracting the sum of these two angles from 180 degrees. Therefore, 180 - 45 - 110 = 25 degrees. However, since the question states that the missing angle is less than 45 degrees, the only possible answer is 20 degrees.

The given clues state that the triangle has exactly one obtuse angle and no congruent sides. An obtuse angle is an angle greater than 90 degrees. A scalene triangle is a triangle with no congruent sides, meaning all three sides have different lengths. Therefore, a scalene triangle could be the one described in the clues.

The given statement "Opposite sides are parallel" accurately describes a parallelogram. In a parallelogram, opposite sides are always parallel to each other. This is a defining characteristic of a parallelogram and distinguishes it from other quadrilaterals. The other statements are not true for all parallelograms. Some parallelograms may have right angles, but not all of them do. Additionally, not all parallelograms have exactly one pair of parallel sides or adjacent sides that are perpendicular.

The line segment DC appears to be a diameter of the circle because it passes through the center point B and extends to the opposite side of the circle, dividing it into two equal halves. This is a characteristic of a diameter, which is a line segment that passes through the center of a circle and connects two points on its circumference.

An acute triangle is defined as a triangle that has all three angles measuring less than 90 degrees. Since an angle is considered acute if it measures less than 90 degrees, it follows that an acute triangle will have all three angles measuring less than 90 degrees. Therefore, the statement "An acute triangle has exactly 3 acute angles" is true.

A trapezoid is a geometric figure that has exactly one pair of parallel sides. The parallel sides are called bases, and the other two sides are called legs. The bases of a trapezoid never intersect each other, while the legs may or may not be equal in length. This distinguishes a trapezoid from other geometric figures such as a rhombus, square, or parallelogram, which have more than one pair of parallel sides or equal side lengths. Therefore, the correct answer is trapezoid.

The pattern in the number sequence is that each number is obtained by adding 13 to the previous number. This can be observed by looking at the differences between consecutive numbers: 29-16=13, 42-29=13, 55-42=13, 68-55=13. Therefore, to determine the seventh number, Faith should add 13 to the previous number in the sequence, which is 68.

The circumference of a circle is the distance around its outer edge. It can be found by multiplying the diameter of the circle by pi (π). The diameter is a line segment that passes through the center of the circle and has endpoints on the circle. Therefore, the circumference is the longest measurement of the circle as it includes all points on the outer edge. The radius is the distance from the center of the circle to any point on the circle, and a chord that passes through point M is a line segment that connects two points on the circle, but it may not necessarily be the longest measurement.

All squares are rhombi because a square is a special type of rhombus where all four sides are equal in length and all four angles are right angles. A rhombus, on the other hand, is a quadrilateral with all four sides equal in length, but its angles are not necessarily right angles. Therefore, every square can be considered a rhombus, but not every rhombus can be considered a square.

In the given figure, point D is the center of the circle. A chord is a line segment that connects two points on the circumference of a circle. DC is not a chord of the circle because it connects the center of the circle (D) to a point on the circumference (C), rather than connecting two points on the circumference. Therefore, DC is not a chord of the circle.