n this article,we had described Which pair of triangles can be proven congruent by SAS.Two triangles are shown with the same angle measurements. The second triangle has been shifted to its right and placed upright so that each side corresponds with a corresponding side of first figure, creating an isosceles pair. Rotating one of these figures about their shared base point will produce another identical version.
A proof of the fact for this first figure is as follows: Let “ABC” denote the first figure, with corresponding angles labeled as “α”, “β” and “γ”. Construct an inverted equilateral triangle that forms two line segments, one from each vertex to the opposite base corner. Label these line segments as shown in Figure 2. Label line segment “AB” as
“x”, label line segment “AC” as
“y”, and denote the point where they intersect as “O”.
To prove that each corresponding side of triangle “ABC” is congruent to its counterpart in inverted triangle “A’B’C'”:
Two triangles are shown. One has a side that’s shared with another, while the other has two congruent angles and respective sides Next to this illustration are written three equalities which can be used for solving these types of puzzle arrangements in circumference or diameter formulae.
Two right triangles are shown above. The first has an angle that is congruent to 90 degrees and shares a side with its corresponding second triangle, while the other two sides of each individual figure form respective angles between them at 45-degree intervals beyond those which would result from just looking solely within it alone; but when these thirds combined together follow one another across shared edges until finally coming full circle back around again–they become mirror images.
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Answers
1.) (Ex. 1) sin 30 = tan 60
(Ex. 2) cos 30 = cot 60
2.) (tan x)(cos x) = (adjacent/hypotenuse)(hypotenuse/opposite) = 1
3.) (sec x)(csc x) = (hypotenuse/adjacent)(opposite/hypotenuse) = 1
4.) (sin x)(cos x) = (opposite/hypotenuse)(adjacent/hypotenuse) = 1
5.) sin y = cos x ; tan y = cot x
6.) cos y = sin x ; cot y = tan x
7.) (sec x)(tan x) = (hypotenuse/opposite)(adjacent/hypotenuse) = cos x
8.) sin x = 3/5; tan 30° = 2.5
3x – 5(sqrt.(3^2)+1) = 2.52
x = 13.15 degrees
3x – 5(5.65) = 2.512
4x = 17.75 ; x = 4.33 radians or 6 degrees
9.) sin y = cos z ; cot y = tan z
cosecant (Cos-1y) = cosine of tangent (tan-1y)
10.) sin y = (a/6) ; cot y = (a/12)
C on the EDGE
It’s an easy way to remember that, when solving problems or doing math in any subject matter you should always be careful with your answers. Make sure they add up correctly before moving onto another question.
Step-by-step explanation:
Sorry, I’m so confused
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