Question

If two corresponding interior angles of two triangles are congruent, how do you know that the triangles are similar?(1 point)
Responses

Since two corresponding interior angles are congruent, the sides opposite the angles are congruent. The remaining pair of sides must also be congruent. The triangles are similar by SSS criterion.
Since two corresponding interior angles are congruent, the sides opposite the angles are congruent. The remaining pair of sides must also be congruent. The triangles are similar by SSS criterion.

Since two corresponding interior angles are congruent, the sides opposite the angles are congruent. The triangles are similar by SAS criterion.
Since two corresponding interior angles are congruent, the sides opposite the angles are congruent. The triangles are similar by SAS criterion.

Since the sum of angle measures in a triangle is 360°
, the third angle pair must have the same measure and are thus congruent. Because all three corresponding interior angles of the triangle are congruent, the triangles are similar by the definition of similarity.
Since the sum of angle measures in a triangle is 360 degrees, the third angle pair must have the same measure and are thus congruent. Because all three corresponding interior angles of the triangle are congruent, the triangles are similar by the definition of similarity.

Since the sum of angle measures in a triangle is 180°
, the third angle pair must have the same measure and are thus congruent. Because all three corresponding interior angles of the triangle are congruent, the triangles are similar by the definition of similarity.


Point upper A is on line upper Y upper X. Point upper B is on diagonal upper Y upper Z. A small square box is marked in angle upper A and angle upper X.



If △XYZ ∼ △AYB
, and YB=25
ft, YA=16
ft, and YZ = 88
ft, then what is the length of YX¯¯¯¯¯¯¯¯
?

(1 point)
Responses

79 ft.
79 ft.

137.5 ft.
137.5 ft.

56.32 ft.
56.32 ft.

67.6 ft.


Point upper D is marked at the midpoint of side upper A upper B. Segments upper A upper D and upper D upper B are marked with single congruent tick marks. Point upper E is marked at the midpoint of side upper B upper C. Segments upper B upper E and upper E upper C have congruent triple tick marks. Point upper F is marked at the midpoint of side upper A upper C. Segment upper A upper F and upper F upper C have congruent double tick marks. Three lines connect midpoints upper D to upper E, upper D to upper F, and upper F to upper E, forming a second triangle.


Image Long DescriptionPoint upper D is marked at the midpoint of side upper A upper B. Segments upper A upper D and upper D upper B are marked with single congruent tick marks. Point upper E is marked at the midpoint of side upper B upper C. Segments upper B upper E and upper E upper C have congruent triple tick marks. Point upper F is marked at the midpoint of side upper A upper C. Segment upper A upper F and upper F upper C have congruent double tick marks. Three lines connect midpoints upper D to upper E, upper D to upper F, and upper F to upper E, forming a second triangle.

Given the image, which statement must be true?

(1 point)
Responses

DF=12BC
upper D upper F equals Start Fraction 1 over 2 End Fraction upper B upper C

DE=12AB
upper D upper E equals Start Fraction 1 over 2 End Fraction upper A upper B

BC=2EF
cap b cap c is equal to 2 cap e cap f

2DF=AC

Answer 1

1) Since the sum of angle measures in a triangle is 180°, the third angle pair must be congruent; with all three corresponding angles congruent the triangles are similar (AA).

2) 56.32 ft.

3) DF = 1/2 BC.