Aconjecture and the flowchart proof used to prove the conjecture are shown.
given: ab || xc
prove: m∠1 + m∠2 + m∠3 = 180°

drag and drop each statement to each box to complete the proof

∠1 + ∠2 + ∠3 = 180°

Step-by-step explanation:

Given :  AB II XC

To Show : ∠1 + ∠2 + ∠3 = 180°

Proof: Here, given that AB is parallel to the line XC

⇒  ∠4  =  ∠2  (Pair of Alternate angles as AB II XC)    (1)

and ∠5  =  ∠3 (Pair of Alternate angles as AB II XC)  (2)

Now, ∠1 + ∠4 + ∠5  = 180° ( Straight Angle)

But, from above (1) and (2)

∠1 + ∠2 + ∠3   =   180°  ( as ∠4  =  ∠2,  ∠5  =  ∠3)

Hence, ∠1 + ∠2 + ∠3   =   180°

Hence Proved.

there is no question content here, but you for the free points! : d

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.