Question

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.

Answer 1

The three statements that are true are:

1. Vertical angles prove that Angle 2 is congruent to angle 5.
2. The triangles are similar because corresponding sides are congruent.
3. In the two similar triangles, Angle 1 and Angle 4 are alternate interior angles.

Answer 2

the three option that are ture:

.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.

.The triangles are similar because corresponding sides are congruent.

Explanation:

Clearly! Let's go through each statement and explain why it's true grounded on the given information

1. Vertical angles prove that Angle 2 is harmonious to angle 5

Vertical angles are formed when two lines intersect. They're contrary each other and always harmonious. In this case, Angle 2 and Angle 5 are perpendicular angles because they're contrary each other and formed by the crossroad of lines d andp. thus, Angle 2 is harmonious to Angle 5.

2. In the two analogous triangles, Angle 1 and Angle 4 are alternate interior angles

Alternate interior angles are formed when a transversal intersects two resemblant lines. In this case, lines d and c are resemblant, and they're bisected by lines q andp. Within the triangles formed( let's call them Triangle 1 and Triangle 2), Angle 1 and Angle 4 are formed by the crossroad of line q and the resemblant lines. Since lines d and c are resemblant, Angle 1 and Angle 4 are alternate interior angles and thus harmonious.

3. The triangles are analogous because corresponding sides are harmonious

Two triangles are considered analogous if their corresponding angles are harmonious and their matching sides are commensurable. In this case, the given angles( Angle 1, Angle 2, Angle 3, Angle 4, Angle 5, Angle 6) and their connections indicate that Triangle 1 and Triangle 2 have harmonious corresponding angles. also, since lines d and c are resemblant, the corresponding sides formed by those lines and the cutting lines( q and p) are commensurable. thus, grounded on the given information, the triangles are analogous.

These explanations show how the given information and geometric parcels lead to the verity of the statements.