Line RS intersects triangle BCD at two points and is parallel to segment DC. Triangle B C D is cut by line R S. Line R S goes through sides D B and C B. Lines D C and R S are parallel. width= Which statements are correct? Select three options. △BCD is similar to △BSR. StartFraction B R Over R D EndFraction = StartFraction B S Over S C EndFraction If the ratio of BR to BD is Two-thirds, then it is possible that BS = 6 and BC = 3. (BR)(SC) = (RD)(BS) StartFraction B R Over R S EndFraction = StartFraction B S Over S C EndFraction

The correct options are;

1) ΔBCD is similar to ΔBSR

2) BR/RD = BS/SC

3) (BR)(SC) = (RD)(BS)

Step-by-step explanation:

1) Given that RS is parallel to DC, we have;

∠BDC = ∠BRS (Angles on the same side of transversal)

Similarly;

∠BCD = ∠BSR (Angles on the same side of transversal)

∠CBD = ∠CBD = (Reflexive property)

Therefore;

ΔBCD ~ ΔBSR Angle, Angle Angle (AAA) rule of congruency

2) Whereby  ΔBCD ~ ΔBSR, we therefore have;

BC/BS = BD/BR → (BS + SC)/BS = (BR + RD)/BR = 1 + SC/BS = RD/BR + 1

1 + SC/BS = 1 + RD/BR = SC/BS = 1 + BR/RD - 1

SC/BS = RD/BR

Inverting both sides

BR/RD = BS/SC

3) From BR/RD = BS/SC the above we have by cross multiplication;

BR/RD = BS/SC gives;

BR × SC = RD × BR → (BR)(SC) = (RD)(BR).

This question is related to properties of similar figures. Therefore, the three statements that are correct are:

Two or more figures or shapes are said to be similar if they have all properties in common. This implies angles, orientation and parallel/ perpendicular sides etc.

Comparing the properties of the sketch for the question, the required statements that are correct are:

a. ΔBCD is similar to ΔBSR  

b. =

c. (BR)(SC) = (RD)(BS)

The sketch for the question is attached for better comparison.

Visit: link

step-by-step explanation:

you can add the two numbers and divide the result by 2. or you can find the gap between the two numbers and add half of this to the smaller number.

the answer is y = 11.54

hope this : )