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
To find the distance between S and T, we can use the proportion:
(Side PR / Side PQ) = (Side RT / Side ST)
Plugging in the given values:
(36 km / 48 km) = (81 km / ST)
Cross-multiplying:
36 km * ST = 48 km * 81 km
Simplifying:
36 km * ST = 3,888 km
Dividing both sides by 36 km:
ST = 108 km
Therefore, the distance between S and T is 108 km.
Right triangle ABC is shown below.
On a coordinate plane, a line goes through (negative 1, 0) and (0, 3). A triangle has a rise of 3 and run of 1.
A similar right triangle would be created by a run of 4 and a rise of
.
A similar right triangle would be created by a rise of 12.
This can be calculated using the concept of similarity, where the corresponding sides of similar triangles are proportional.
The ratio of the rise to the run in the given triangle is 3:1. In a similar triangle, the ratio of the rise to the run would be the same.
Therefore, if the run is 4, the rise would be 3 times 4, which is 12.
Line l is parallel to line e in the figure below.
Parallel lines e and l are crossed by lines m and n to form 2 triangles. At the intersection of parallel line e with line n is angle q, and with line m is angle 3. Angle 2 is the third angle. At the intersection of parallel line l and m is 6, at line n is 4. The third angle is 5.
Which statements about the figure are true? Check all that apply.
Vertical angles prove that Angle 1 is congruent to angle 4.
Vertical angles prove that Angle 2 is congruent to angle 5.
The triangles are similar because corresponding sides are congruent.
The triangles are similar because alternate interior angles are congruent.
In the similar triangles, Angle 3 and Angle 6 are alternate interior angles.
In the similar triangles, Angle 3 and Angle 4 are corresponding angles.
The following statements about the figure are true:
1. Vertical angles prove that Angle 1 is congruent to angle 4.
2. Vertical angles prove that Angle 2 is congruent to angle 5.
3. The triangles are similar because corresponding sides are congruent.
Line v is parallel to line w.
Parallel lines v and w are crossed by lines s and t to form 2 triangles. At parallel line v, the angle formed by line t is 1 and formed by line s is 2. At parallel line w, the angle formed b line is 4 and line t is 5. Angles 3 and 6 are formed by s and t.
Which set of statements about the angles is true?
Angle 1 is congruent to angle 6, angle 2 is congruent to angle 4, angle 3 is congruent to angle 5
Angle 1 is congruent to angle 5, angle 2 is congruent to angle 4, angle 3 is congruent to angle 6
Angle 6 is congruent to angle 2, angle 5 is congruent to angle 4, angle 1 is congruent to angle 3
Angle 6 is congruent to angle 1, angle 3 is congruent to angle 2, angle 4 is congruent to angle 5
The set of statements about the angles that is true is:
Angle 1 is congruent to angle 5, angle 2 is congruent to angle 4, angle 3 is congruent to angle 6.
Side V W is parallel to Side Y Z in the map below.
Triangle V X W. Side V W is 4 miles and side V X is 3 miles. Triangle X Z Y. Side X Z is 9 miles and side Y Z is x miles.
Which proportion solves for the distance between Y and Z?
StartFraction 3 Over 9 EndFraction = StartFraction 4 Over x EndFraction
Three-fourths = StartFraction x Over 9 EndFraction
Four-thirds = StartFraction 9 Over x EndFraction
StartFraction 3 Over x EndFraction = StartFraction 4 Over 9 EndFraction
The proportion that solves for the distance between Y and Z is:
StartFraction 3 Over x EndFraction = StartFraction 4 Over 9 EndFraction.
Side A B is parallel to Side D E in the map below.
Triangle A B C. Side A B is 15 feet and side B C is 9 feet. Triangle C D E. Side C D is 6 feet and side D E is x feet.
Which proportion solves for the distance between D and E?
StartFraction 9 Over 6 EndFraction = StartFraction x Over 15 EndFraction
StartFraction 6 Over x EndFraction = StartFraction 15 Over 9 EndFraction
StartFraction 9 Over 6 EndFraction = StartFraction 15 Over x EndFraction
StartFraction 6 Over 15 EndFraction = StartFraction 9 Over x EndFraction
The proportion that solves for the distance between D and E is:
StartFraction 6 Over x EndFraction = StartFraction 15 Over 9 EndFraction.
The graph shows a line and two similar triangles.
On a coordinate plane, a line goes through (0, 0) and (6, 10). A small triangle has a rise of 5 and run of 3, and a larger triangle has a rise of 10 and run of 6.
What is the equation of the line?
y = 5 x
y = 3 x
y = three-fifths x
y = five-thirds x
To find the equation of the line, we can use the slope-intercept form:
y = mx + b
where m is the slope and b is the y-intercept.
To find the slope, we can use the formula:
m = (change in y) / (change in x)
Given the points (0, 0) and (6, 10), the change in y is 10 - 0 = 10, and the change in x is 6 - 0 = 6.
Plugging the values into the formula:
m = 10/6 = 5/3
So, the slope of the line is 5/3.
Plugging the slope into the slope-intercept form, and using the point (0, 0), we can find the y-intercept:
0 = (5/3)(0) + b
0 = b
Therefore, the y-intercept is 0.
Putting it all together, the equation of the line is:
y = (5/3) x