Triangle ABC is congruent to triangle DEF. If DE = 41, EF = 23, DF = 36, and AB = 8x − 7, what is x? Round to the nearest tenth.
2 answers:
The side AB is equal to the side DE. Then the value of x is 6.
<h3>What is the triangle?</h3>A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
Triangle ABC is congruent to triangle DEF.
If DE = 41, EF = 23, DF = 36, and AB = 8x − 7.
Then the side AB is equal to the side DE.
AB = DE
8x - 7 = 41
8x = 48
x = 6
Then the value of x is 6.
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Option A AY || XV given that A, Y, Z are midpoints of sides XW, VW, XV respectively. This can be obtained by knowing what similar triangles are and finding which sides are proportional.
<h3>Find the correct option:</h3>Similar triangles: If two triangles have proportional sides the are similar.
For example, if ΔABC and ΔDEF are similar then
∠ABC = ∠DEF and ∠ACB = ∠DFE
Then we can write that, ΔABC ~ ΔDEF
Here in this question,
Since A, Y, Z are midpoints of sides XW, VW, XV
XA = AW
WY = VY
XZ = VZ
To consider sides AY and XV we should take triangles ΔWAY and ΔWXV
(since A is the midpoint of WX)
(since Y is the midpoint of WV)
∠AWY = ∠XWV (reflexive property)
Therefore ΔWAY and ΔWXV are similar triangles
= 2
∠WAY = ∠WXV and ∠AYW = ∠XVW
Hence,
AY || XV option A AY || XV given that A, Y, Z are midpoints of sides XW, VW, XV respectively.
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Disclaimer: The question was given incomplete on the portal. Here is the complete question.
Question: Analyze the diagram below and answer the question that follows. If Z, Y and A are midpoints of ΔVWX what is true about AY and XY?
A. AY || XV
B. 1/2 AY = XV
C. AY = XV
D. AY ≅ XV
