The figure below shows parallel lines cut by a transversal:
A pair of parallel lines is shown with arrowheads on each end. A transversal cuts these two lines. An angle formed between the top parallel line and the transversal on the outer right side is marked 1. Another angle formed between the top parallel line and the transversal on the inner left side is marked 2
Which statement is true about ∠1 and ∠2? (5 points)
∠1 and ∠2 are congruent because they are a pair of vertical angles.
∠1 and ∠2 are congruent because they are pair of corresponding angles.
∠1 and ∠2 are complementary because they are a pair of vertical angles.
∠1 and ∠2 are complementary because they are pair of corresponding angles.
∠1 and ∠2 are congruent because they are a pair of vertical angles.
wo similar triangles are shown below:
Two triangles are shown. The sides of the triangle on the left are marked 6, 8, 4. The sides of the triangle on the right are marked as 3, 4, and 2. For the triangle on the left, the angle between sides marked 8 and 6 is labeled as a, marked by a double arc, and the angle between the sides marked 8 and 4 is labeled as b, marked by a single arc. The third angle is marked by a triple arc. For the triangle on the right, the angle between sides marked 2 and 4 is labeled as c, marked by a single arc and the angle between the sides marked 4 and 3 is labeled as d, marked by a double arc. The angle between the sides 2 and 3 is labeled as e, marked by a triple arc, and it is also the angle on the top vertex of this triangle.
Which two sets of angles are corresponding angles? (5 points)
∠a and ∠d; ∠b and ∠c
∠a and ∠e; ∠b and ∠d
∠a and ∠c; ∠b and ∠d
∠a and ∠e; ∠b and ∠c
∠a and ∠c; ∠b and ∠d
A student writes an incorrect step while checking if the sum of the measures of the two remote interior angles of triangle ABC below is equal to the measure of the exterior angle.
A triangle ABC is shown. The base of the triangle extends into a straight line. The angle formed between this straight line and the edge of the triangle is marked as p. The angle adjacent to w is marked as o, and the other two angles inside the triangle are marked as m and n.
Step 1: m∠m + m∠n + m∠o = 180 degrees (sum of angles of a triangle)
Step 2: m∠p − m∠o = 90 degrees (alternate interior angles)
Step 3: Therefore, m∠m + m∠n + m∠o = m∠o + m∠p
Step 4: So, m∠m + m∠n = m∠p
In which step did the student first make a mistake and how can it be corrected? (5 points)
Step 1; it should be m∠m + m∠n + m∠o = 90 degrees (corresponding angles)
Step 1; it should be m∠m + m∠n + m∠o = 90 degrees (adjacent angles)
Step 2; it should be m∠o + m∠p = 180 degrees (alternate exterior angles)
Step 2; it should be m∠o + m∠p = 180 degrees (supplementary angles)