Line r is parallel to line c.
Parallel lines r and c are crossed by lines x and y to form 2 triangles. At parallel line r, the angle formed by x is 5 and the angle formed by y is 4. At parallel line c, the angle formed by x is 3 and the angle formed by y is 2. Angles 1 and 6 are at the intersection of lines x and y.
Which angle is congruent to Angle 3?
Angle 2
Angle 4
Angle 5
Angle 6
Angle 5 is congruent to Angle 3.
Line p is parallel to line q.
Parallel lines p and q are crossed by lines a and b to form 2 triangles. At parallel line p, angle 4 is formed by line b and angle 5 is formed by line a. Angle 6 is the third angle. At parallel line q, angle 3 is formed by line 3 and angle 2 is formed by line b. Angle 1 is the third angle.
Which set of statements about the angles is true?
Angle 1 is congruent to angle 6, angle 5 is congruent to angle 4, angle 3 is congruent to angle 2
Angle 2 is congruent to angle 4, angle 3 is congruent to angle 6, angle 1 is congruent to angle 5
Angle 3 is congruent to angle 6, angle 1 is congruent to angle 2, angle 5 is congruent to angle 4
Angle 6 is congruent to angle 1, angle 5 is congruent to angle 3, angle 4 is congruent to angle 2
The correct set of statements about the angles is:
Angle 3 is congruent to angle 6, angle 1 is congruent to angle 2, angle 5 is congruent to angle 4.
Triangle MNO is similar to triangle RPO.
Triangle M N O. Side M N is 20 kilometers and side M O is 32 kilometers. Triangle R P O. Side O R is 48 kilometers.
Valek finds the distance between P and R. His work is shown below.
Step 1 StartFraction 32 Over 48 EndFraction = StartFraction 20 Over P R EndFraction
Step 2 20 P R = (32) (48)
Step 3 20 P R = 1,536
Step 4 P R = 76.8 kilometers
What is Valek’s first error?
Valek did not correctly divide 1,536 by 20 going from step 3 to step 4.
Valek did not find the correct product of 32 and 48 going from step 2 to step 3.
Valek should have written the proportion in step 1 as StartFraction 32 Over 20 EndFraction = StartFraction P R Over 48 EndFraction.
Valek should have written the cross-product in step 2 as 32 P R = (20) (48).
Valek's first error is: Valek did not correctly divide 1,536 by 20 going from step 3 to step 4.
Line k is parallel to line l.
Lines k and l are parallel. Lines m and n intersect to form 2 triangles. The top triangle has angles 1, 2, 3 and the bottom triangle has angles 4, 5, 6.
Which angle is congruent to Angle 4?
Angle 1
Angle 2
Angle 5
Angle 6
Angle 5 is congruent to Angle 4.
Line d is parallel to line c in the figure below.
Parallel lines d and c are intersected by lines q and p to form 2 triangles. At lines d and p, the angle is 2, at d and q, the angle is 1, and at q and p the angle is 3. At lines c and q, the angle is 4, at p and c, the angle is 5, and the third angle is 6.
Which statements about the figure are true? Select three options.
Vertical angles prove that Angle 2 is congruent to angle 5.
In the two similar triangles, Angle 1 and Angle 4 are alternate interior angles.
Vertical angles prove that Angle 3 is congruent to angle 6.
The triangles are similar because alternate interior angles are congruent.
In the two similar triangles, Angle 2 and Angle 4 are corresponding angles.
The triangles are similar because corresponding sides are congruent.
The three true statements about the figure are:
1. Vertical angles prove that Angle 2 is congruent to angle 5.
2. In the two similar triangles, Angle 1 and Angle 4 are alternate interior angles.
3. The triangles are similar because corresponding sides are congruent.
In the map below, Side P Q is parallel to Side S T.
Triangle P Q R. Side P Q is 48 kilometers and side P R is 36 kilometers. Triangle S R T. Side R T is 81 kilometers.
What is the distance between S and T? If necessary, round to the nearest tenth.
21.3 km
60.8 km
108 km
117 km