Measure of the some angles in the figure are given.
Prove that,
AP/AB = AQ/QC

Step-by-step explanation:

Given that

In ∆ ABC, PQ is a line drawn on AB and AC

In ∆ APQ and ∆ ABC

∠ APQ = ∠ ABC = 60°

∠ PAQ = ∠ BAC (Common vertex angle )

By AA similarity criteria

∆ APQ and ∆ ABC are similar triangles

=> ∆ APQ ~ ∆ ABC

We Know that

If two polygons of same number of sides are said to be similar,

If the corresponding angles are equal.

If the corresponding sides are in the same ratio or in proportion.

So, The corresponding angles are mist be in proportion

=> AP / PB = AQ/QC

Hence, Proved.

If two polygons of same number of sides are said to be similar,

If the corresponding angles are equal.

If the corresponding sides are in the same ratio or in proportion.

If PQ || BC then by Basic Proportionality Theorem, AP/PB = AQ/QB

If a line drawn parallel to one side of a triangle intersecting other two sides at two different points and the line divides the other sides in the same ratio.

8496 cars

step-by-step explanation:

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.