Recent questions in Angle theorems

Maia Pace
2022-08-15

Let A, B, C, be points on a line l, and let A′, B′, C′ be points on a line m. Assume AC′∥A′C and B′C∥BC′. Show that AB′∥A′B.

Jenny Stafford
2022-08-14

Angle theorems
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gladilkamwy
2022-08-14

Let ABC be an acute triangle with circumcenter O and let K be such that KA is tangent to the circumcircle of $\mathrm{\u25b3}ABC$ and $\mathrm{\angle}KCB={90}^{\circ}$. Point D lies on BC such that KD||AB. Show that DO passes through A.

Angle theorems
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popljuvao69
2022-08-14

In triangle $ABC,AB>AC$. D is a point on AB such that $AD=AC$.

Prove that $\phantom{\rule{thinmathspace}{0ex}}\mathrm{\angle}ADC=\frac{\mathrm{\angle}B+\mathrm{\angle}C}{2}$ and $\mathrm{\angle}BCD=\frac{\mathrm{\angle}C-\mathrm{\angle}B}{2}$.

Solving this problem in Euclidean geometry is very easy. But how can it be solved with the following restrictions?

1) Parallel postulate (i.e. properties of parallel lines ) cannot be used.

2) Theorems proved using properties of parallel lines cannot be used.

3) The problem has to be solved the way euclidean geometry problems are solved. Cartesian Geometry cannot be used.

If not solvable, why cannot be?

Angle theorems
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dredyue
2022-08-13

A and B are both obtuse angles such that $\mathrm{sin}(A)=\frac{5}{13}$ and $\mathrm{tan}B=\frac{-3}{4}$. Find exact values for $\mathrm{sin}(A+B)$.

Assuming that the pythagorean theorem is used to answer the question, how is it possible that the values for $\mathrm{tan}B=\frac{-3}{4}$? (That is, a 3-4-5 right angle triangle... how can a side be negative?)

Angle theorems
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ahredent89
2022-08-13

Suppose the triangles ABC and DEF share the circuncircle C, and P and Q are any diferent points on C. Let l, m be, the Simson lines of P related to ABC and DEF, and p, q the Simson lines of Q related to ABC and DEF, then i must prove the angle between l and m equals the angle between p and q.

I just have one Theorem about the Simson line:

Theorem: Let P, Q be two points on the circuncircle, C, of the triangle ABC. Let l, m be their respective Simson's lines. Then the angle between l an m equals to the half of the central angle POQ, where O is the center of C.

Angle theorems
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makeupwn
2022-08-13

O is the center of the semicircle, if $\mathrm{\angle}EOD={45}^{\circ}$ and $OD=AB$, find $\mathrm{\angle}BAC$

Angle theorems
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Moselq8
2022-08-12

I have an integral that is an average of some (unknown) function f over solid angle: $\overline{f}=\frac{1}{4\pi}\underset{\mathrm{\Omega}}{\iint}f\mathrm{sin}\theta \text{}\mathrm{d}\theta \text{}\mathrm{d}\varphi $

Angle theorems
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Brandon Monroe
2022-08-12

Consider the triangle ABC with angle A being 70 degrees, and the side lengths satisfying:

$B{C}^{2}=AC(AB+AC)$

Is there any intuitive way of finding the measure of angle B?

Angle theorems
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Sydney Stein
2022-08-12

Given the Pythagoras Theorem: ${a}^{2}+{b}^{2}={c}^{2}$

Is there a way to get the value of b when we only have a value for a and the angle $\alpha $?

Angle theorems
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Filipinacws
2022-08-12

Hilbert, in Foundations of Geometry briefly mentions that the existence of right angles is a corollary to the supplementary angle theorem. (i.e. If two angles are congruent, then their supplementary angles are congruent).

How does existence of right angles follow from this?

Angle theorems
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betterthennewzv
2022-08-11

Angle theorems
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tamkieuqf
2022-08-11

$AB=AC$

$AD=BC$

$\mathrm{\angle}BAC={20}^{\circ}$

Find $\alpha $.

Angle theorems
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polynnxu
2022-08-10

In triangle ABC, angle bisectors $\overline{AD},$, $\overline{BE},$, and $\overline{CF}$ meet at I. If $DI=3,$, $BD=4,$, and $BI=5,$, then compute the area of triangle ABC.

Angle theorems
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sarahkobearab4
2022-08-10

Angle theorems
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spainhour83lz
2022-08-08

Angle theorems
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Meossi91
2022-08-05