Assume you measured <3 and <5 and found them to be equal. Use the spaces provided below to complete a formal proof that demonstrates the picture is level with the trim.

1. S is a straight line that cuts through f and t

2. Given

3. ∠5 ≅ ∠7

4. ∠7 ≅ ∠3 Corresponding angles

Solution:

Step 1: Given

S is a straight line that cuts through f and t

Step 2: Given

∠3 ≅ ∠5

Alternate interior angles are equal.

Step 3: By Vertical angle theorem

Vertically opposite angles are congruent.

∠5 ≅ ∠7

Step 4: Corresponding angles

∠7 and ∠3 are corresponding angles.

∠7 ≅ ∠3

Step 5: Corresponding angles theorem

f || t

Hence proved.

answer: the answer is one of

step-by-step explanation:   we are given to write a proper fraction where the whole is divided into an even number of equal parts less than ten, and an odd number of those parts exist.

an even number less than 10 may be one of 2, 4, 6 or 8. so, the whole may be one of these four evens.

now, an odd number of these parts must exist, so the numerator must be an odd number, one of 1, 3, 5 or 7. it cannot be 9 because then the fraction will become improper.

thus, our fraction may be one of the following

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1