Question

In the figure angle ACB is a right angle A C equals to CD and c d e f is a rectangle and Angle B A C equals to 50 degree calculate angle bdc and angle between the diagonals C PDF of the rectangle

Answer 1

Answer:

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Step-by-step explanation:

Given: For triangle ABC, angle ABC = 90 degrees, and side AC has a length of 15.

So, we have a shape that looks something like this . . .

Image

. . . where the legs of the triangle can vary AND the location of point D can vary.

Statement 1: Triangle ABC is isosceles.

Since there is ONLY ONE isosceles right triangle with hypotenuse 15, this statement LOCKS triangle ABC into having one and only one shape.

Image

However, statement 1 does NOT lock in the location of point D.

Since this statement does not lock in the location of point D, the length of BD is NOT LOCKED IN.

Consider these two examples.

Image

Image

Notice the different lengths of line segment BD

Since statement 1 does not lock in the length of line segment BD, it is NOT SUFFICIENT

Statement 2: Line segment BD is perpendicular to side AC.

This statement locks in the location of point D (in relation to the triangle's hypotenuse), but it does NOT lock in the shape of the triangle.

Consider these two examples:

Image

Image

Notice the different lengths of line segment BD

Since statement 2 does not lock in the length of line segment BD, it is NOT SUFFICIENT

Statements 1 and 2 combined

Statement 1 locks in the shape of triangle ABC.

Statement 2 then locks in the location of point D as follows:

Image

Since there's only one diagram that can be drawn with the given information, there can be ONLY ONE length of line segment BD

Are we required to find this length? No. We need only recognize that there can be only one length.

Since we can answer the target question with certainty, the combined statements are SUFFICIENT