Match each set of conditions with the corresponding relationship between ∆abc and ∆xyz and the criterion (if any) that proves the relationship. tiles ab = xy, bc = yz, and angle b is congruent to angle y. ∆abc and ∆xyz are congruent by the sss criterion. ab = xy, and angles a and b are congruent to angles x and y, respectively. ∆abc and ∆xyz are not necessarily congruent. angles a, b, and c are congruent to angles x, y, and z, respectively. ∆abc and ∆xyz are congruent by the sas criterion. ab = xy, bc = yz, and ca = zx. ∆abc and ∆xyz are congruent by the asa criterion. pairs arrowboth arrowboth arrowboth arrowboth

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).

d. it is a convex pentagon because it has five sides and none of the sides would extend into the inside of the polygon.

step-by-step explanation: