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 th
rough 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
1 answer:
Answer:
The correct statements are;
1) ΔBCD is similar to ΔBSR
2) BR/RD = BS/SC
3) (BR)(SC) = (RD)(BS)
Step-by-step explanation:
1) Since RS is parallel to DC, we conclude that;
∠BDC = ∠BRS (Angles formed on the same side of the transversal)
Furthermore;
∠BCD = ∠BSR (Angles formed on the same side of the transversal)
∠CBD = ∠CBD (Reflexive property)
Thus;
ΔBCD ~ ΔBSR by the Angle-Angle-Angle (AAA) similarity criterion.
2) Given that ΔBCD ~ ΔBSR, we obtain;
BC/BS = BD/BR → (BS + SC)/BS = (BR + RD)/BR = 1 + SC/BS = RD/BR + 1
1 + SC/BS = 1 + RD/BR thus, SC/BS = 1 + BR/RD - 1
SC/BS = RD/BR
By inverting both sides we find;
BR/RD = BS/SC
3) From BR/RD = BS/SC, we apply cross multiplication;
BR/RD = BS/SC leads to;
BR × SC = RD × BS → (BR)(SC) = (RD)(BS).
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Answer:
Red paint will cover 262 square feet
of the ramp.Step-by-step explanation:
The lateral surface area represents the surface area of the sides of the ramp without including the top and bottom surfaces
This ramp has three surfaces
The two sides are triangular with dimensions of length 20 and height 8.5
The back consists of a rectangular shape with length 12 and height 8.5
Step 1: Calculating the Area of Triangle
The area of the triangular side =
The area of the triangle =
The area of the triangle =
Thus, the area of the triangle = 85 square feet
Area of both triangles = = 170
Step 2: Finding the Area of Rectangle
Area of rectangle =
therefore,
Area of the rectangular back = = 102 square feet
Step 3: Calculating the total lateral surface area
Overall Lateral Surface Area
= Area of triangles + Area of Rectangle
= 272 square feet
