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Can Thales' Theorem Help Me Solve My Trapezoid Equation?
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In summary: I don't see an equation you are trying to complete, but what do we know about the opposite interior angles of a cyclic quadrilateral?The opposite interior angles are $\angle E+\angle F=60^{\circ}$, and $\angle G+\angle H=120^{\circ}$.
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MarkFL
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I don't see an equation you are trying to complete, but what do we know about the opposite interior angles of a cyclic quadrilateral?
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lornick
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Sorry don't have an equation, my wording mistake, just trying to calculate the angle of E and F. What I have worked out is the angles of A, B, C, and D. A=70 B=110 C=120 D=60. But have no idea how to calculate E and F. If I turn C and D into a right angle on the outside of the trapezoid I get 30 and if I turn B and A into a right angle on the outside of the trapezoid I get 20. But not sure how to compute this into my E and F. Also I forgot to mention that A and D are parallel lines to B and C. Forgot to draw in the arrows on the line.Thank you for any help in solving this.
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MarkFL
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Since $\overline{AD}\parallel\overline{BC}$, and the trapezoid is cyclic, we know it must be isosceles. So we know $\angle A=60^{\circ}$, if $\measuredangle C=120^{\circ}$.
Thus, we know:
\(\displaystyle \angle E+\angle F=60^{\circ}\)
If we label the two angles at vertex $B$ as $G$ and $H$, we then know:
\(\displaystyle \angle G+\angle H=120^{\circ}\)
Can you find two more equations involving these 4 angles? Hint: add the interior angles of the two triangles making up the trapezoid...:D
Also, to simplify matters, $G$ and $H$ must share a special relationship to $E$ and $F$. ;)
Thus, we know:
\(\displaystyle \angle E+\angle F=60^{\circ}\)
If we label the two angles at vertex $B$ as $G$ and $H$, we then know:
\(\displaystyle \angle G+\angle H=120^{\circ}\)
Can you find two more equations involving these 4 angles? Hint: add the interior angles of the two triangles making up the trapezoid...:D
Also, to simplify matters, $G$ and $H$ must share a special relationship to $E$ and $F$. ;)
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lornick
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[QUOTE Since $\overline{AD}\parallel\overline{BC}$, and the trapezoid is cyclic, we know it must be isosceles. So we know $\angle A=60^{\circ}$, if $\measuredangle C=120^{\circ}$.
I had changed the original degrees and didn't realize I had changed the triangles to equal sides. My triangles are not level only the horizontal lines are level, which leaves me with one obtuse angle and one acute angle. :S so sorry I confused matters, but I didn't want to get into trouble for my question from my teachers. Or am I confused lol.
I had changed the original degrees and didn't realize I had changed the triangles to equal sides. My triangles are not level only the horizontal lines are level, which leaves me with one obtuse angle and one acute angle. :S so sorry I confused matters, but I didn't want to get into trouble for my question from my teachers. Or am I confused lol.
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- #6
I like Serena
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Hi lornick! Welcome to MHB! :)
Thales' theorem may help you.
Thales' theorem: if AC is a diameter, then the angle at B is a right angle.
Thales' theorem may help you.
Thales' theorem: if AC is a diameter, then the angle at B is a right angle.
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lornick
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I like Serena said:
Oh nooo I can't believe it was that simple, I have been trying to calculate it as a acute and obtuse angle (hence my issues). The time when you are doing maths and you start to bash your head against a brick wall, only to realize that the answer was right in front of you lol. Thank you sooooooooo much!
Related to Can Thales' Theorem Help Me Solve My Trapezoid Equation?
1. What is a trapezoid?
A trapezoid, also known as a trapezium, is a quadrilateral with at least one pair of parallel sides. This means that two of its sides are parallel to each other, while the other two sides are not.
2. What are the properties of a trapezoid?
The properties of a trapezoid include having two parallel sides, two non-parallel sides, and four angles. The parallel sides are called bases, while the non-parallel sides are called legs. The angles formed by the bases and legs are referred to as base angles and lateral angles, respectively.
3. How is the area of a trapezoid calculated?
The formula for calculating the area of a trapezoid is A = (1/2)h(b1 + b2), where A is the area, h is the height, and b1 and b2 are the lengths of the two parallel sides (bases). This means that the area is equal to half of the height multiplied by the sum of the lengths of the two bases.
4. What is the difference between a trapezoid and a parallelogram?
A trapezoid and a parallelogram are both quadrilaterals, but they have different properties. The main difference between them is that a trapezoid has only one pair of parallel sides, while a parallelogram has two pairs of parallel sides. Additionally, the angles of a trapezoid may not all be equal, while the angles of a parallelogram are always equal.
5. Can a trapezoid have equal sides?
Yes, a trapezoid can have equal sides. This type of trapezoid is called an isosceles trapezoid. In an isosceles trapezoid, the two non-parallel sides are equal in length, and the two base angles are also equal. The other two angles, formed by the legs and the bases, are equal as well.