2
votes
1answer
123 views
+50

Trying to prove that two angles are congruent in a isosceles trapezoid

I was given this assignment to do the following. Write a paragraph proof for the following scenario. Given: KLMN is an isosceles trapezoid. Prove: ∠LKM is congruent to ∠MNL The thing is that I ...
2
votes
1answer
32 views

$\frac{|| \overline{AM}||}{|| \overline{AB}||}=\frac{|| \overline{AN}||}{|| \overline{AC}||}=\frac{|| \overline{MN}||}{|| \overline{BC}||}$

$\Delta ABC$ is a triangle, $M$ is a point in the segment $\overrightarrow{AB}$ and $N$ is a point in the segment $\overrightarrow{AC}$, such that $\overrightarrow{MN}$ is parallel to ...
0
votes
2answers
55 views

Proving the inscribed angle theorem

I need to prove that a circle's inscribed angle is 1/2 of the arc it intercepts. I am given that one of the chords making up the angle is the diameter. I have an entire project to do based off of this ...
1
vote
1answer
57 views

Proof: Convex set of a quadrilateral is a convex quadrilateral

Prove that $\Box ABCD$ is a convex set whenever $\Box ABCD$ is a convex quadrilateral. Things I know: A set of points $S$ is said to be a convex set if for every pair of points $A$ and $B$ in $S$, ...
0
votes
0answers
9 views

Determining the minimal number of axis to test against in the SAT (Separating Axis Theorem)

Most implementations of the SAT algorithm I've seen involve testing each axis in either shape being tested against for collisions. But I recently implemented the SAT algorithm in python and noticed ...
0
votes
0answers
35 views

2 column proof of The Tangent-Chord Angle Corollary

I need to prove 12.23 on this section (http://i.imgur.com/M5iev9K.png) I can use any of the theorems or corollaries before 12.23 but not the ones after it. This is a list ...
3
votes
2answers
55 views

How to prove the formula of altitude from this following triangle?

Given: Right triangle $\triangle ABC$ with $A$ as right angle. If $t_A$ is altitude that drawn from point $A$ to $\overline{BC}$, called $\overline{AD}$. Prove that $t_A = ...
0
votes
1answer
46 views

How to prove that $DE=EF +DG$ from this following triangle problem?

Given a right triangle $ABC$, where $C$ is a right angle. We choose points $G$ at $AC$ and $F$ at $BC$, and $D$ and $E$ at $AB$. We draw right triangles $AGD$ and $EBF$, such that $\angle AGD= ...
3
votes
2answers
71 views

Is a quadrilateral with one pair of opposite angles congruent and the other pair noncongruent necessarily a kite?

If convex quadrilateral ABCD has congruent angles A and C and the other pair of angles B and D are not congruent, is ABCD necessarily a kite (two pairs of consecutive congruent sides but opposite ...
2
votes
0answers
88 views

Bretschneider-Brahmagupta-Heron Proof

Derive Bretschneider's formula, Brahmagupta's formula and Heron's formula in one memorable elegant proof. I ask this question merely to see the creativity of the MSE community when it comes to ...
3
votes
2answers
129 views

Geodesic equations and christoffel symbols

I want to learn explicitly proof of the proposition 9.2.3. Which books or lecture notes I can find? Please give me a suggestion. Thank you:)
4
votes
3answers
203 views

Proving the Obvious

Is it normal that I have the hardest time when I'm trying to prove statements that are blatantly obvious on a visual and/or intuitive level? For instance, how does one go about formally proving the ...
3
votes
2answers
142 views

Proof of radius of a circle based on an equilateral triangle and a square.

I need help proving this: ABC is an equilateral triangle; $BCDE$ is a square. Both figures have sides of length $2cm$. Pentagon $ACDEB$ lies inside a circle that passes through points $A, D$ and $E$. ...
1
vote
2answers
72 views

In triangle $ABC$ prove that $AB = 2BC$

In solving this proof I am NOT permitted to use any numerically related givens (i.e., the sum of all angles in a triangle is 180 degrees or in a right triangle side Asquared + side Bsquared = side ...
4
votes
3answers
89 views

Proof that a line cuts in half the area of a parallelogram iff it goes through the intersection of the diagonals?

I read a theorem in a book which says that a line bisects a parallelogram iff it goes through the intersection of the diagonals. The edge case of this is of course if the line is one of the diagonal ...
0
votes
1answer
63 views

Proof adding layers of constant width to a shape tends to an $d$-sphere as the number of layers tends to $\infty$

Good night, I've recently seen one of Victoria Hart's videos on Youtube (it wasn't about this, it was about Fibonacci numbers, and I found it on a comment in this site), and in it she said that if ...
1
vote
2answers
69 views

Proof using properties of an isosceles or right-angle triangle

Given a triangle $ABC$ with sides $AB=BC$ and angle$\angle B=100^\circ $, prove that $$a^3 + b^3 = 3a^2b$$ where $a=AB=BC$ and $b=AC$, I have tried to use simultaneously the sine and cosine rules as ...
0
votes
2answers
115 views

proof that the three interior angles of a triangle is congruent to a straight line (without measurements)

I'm trying to essentially prove that the interior angles of a triangle add up to 180 degrees. However, I'm trying to prove it without mentioning measurements of an angle. I think I understand the ...
0
votes
1answer
50 views

Is simple straight-edge and compass construction a substantial proof?

I'm working on a problem that asks to prove that a point $D$ is outside of a $\triangle ABC$, on the circle through the triangle, given that sides $AB$ and $AC$ are not congruent, and that $D$ is the ...
2
votes
1answer
306 views

Proof involving angle bisector in an arbitrary triangle

In the above figure, AD is a bisector angle A (angle BAC). How do I prove in a triangle ABC of any dimensions that, $AB > BD$ $AC > CD$ Is it also possible to prove that, $AB > AD$ ...
1
vote
2answers
48 views

How to prove a line is above another line

Suppose I have the following line: $y=-4x + 80$, for $x \ge 0$ and $y \ge 0$ I want to show that if I vary the slope, $m$ like so: $-4\lt m \le -2$ Then the new line will be above the old line ...
1
vote
4answers
271 views

Parallel Lines Proof

How do you prove that two parallel lines never cross? By definition this is implied, but how do you prove it for any pair of parallel lines? In other words, how do prove that 2 parallel lines will ...
1
vote
1answer
547 views

“Direct Proof” of the Steiner-Lehmus Theorem

The Steiner-Lehmus Theorem is famous for its indirect proof. I wanted to come up with a 'direct' proof for it (of course, it can't be direct because some theorems used, will, of course, be indirect). ...
0
votes
1answer
77 views

Finding the ratio of two sides of a triangle with known angles

I wondered what the ratios between the sides of a triangle is, when the angles are known. So basically: $\triangle ABC$ has angles $\alpha, \beta \text{ and } \gamma$. Find $\frac{\lvert AB ...
0
votes
2answers
1k views

If the diagonals of a trapezoid are congruent, then the trapezoid is isosceles.

Thanks in advance to anyone who can help me out on this. I'm currently a junior in high school taking and doing well my school's honors pre-calc class, but of all of the math I've ever learned, proofs ...
2
votes
1answer
63 views

Can one use Pick's theorm to prove that area size 5 covers at least 6 grid points?

According to Pick's Theorem, the size of an area $A$ can be calculated by the sum of the interior lattice points located in the polygon $i$ and the number of lattice points on the boundary placed on ...
6
votes
0answers
374 views

Proof Strategy for a Dynamical System of Points on the Plane

I have a rather simple-looking system which exhibits a particular behaviour in simulation, and I would now like to attempt to prove this formally. The problem is, I don't really know where to start, ...
3
votes
0answers
1k views

Proof of the sine rule

So I made my first attempt at a proof. I think it turned out well. Maybe not. But I was wondering if someone could take a look at it and tell me what they think. I'd be glad to hear some criticism on ...
5
votes
1answer
295 views

Proof of pythagorean theorem

Any one seen this proof before? $$\frac{d}{dx} \sin(x)^2=2\cos(x)\sin(x)$$ $$\frac{d}{dx} \cos(x)^2=-2\cos(x)\sin(x)$$ $$\frac{d}{dx} \sin(x)^2+\frac{d}{dx} \cos(x)^2=0$$ $$\sin(x)^2+\cos(x)^2=c$$ ...
2
votes
0answers
275 views

On the geometric arguments used in Newton's *Principia Mathematica Naturalis Philosophae*

When one reads Newton's Principia Mathematica, one is immediately aware of the complexity of the synthetic geometry that he uses to prove his propositions. This I understand because all of the ...
0
votes
1answer
1k views

What is CPCTC: Property, definition..?

So we're doing proofs in class and I was wondering: Normally in two-column proofs you need Statements and Reasons, where Reasons are normally postulates, definitions, other theorems, or givens. ...
2
votes
2answers
438 views

Prove there exists a triangle without using Euclidean Parallel Postulate

Let $a$ and $b$ be real numbers where $0 < a< b<180$. Let $A$, $B$, $D$ be points so $A$-$B$-$D$. Part 1: Prove there exists a triangle $ABC$ where measure of angle $CAB$ is $a$ and measure ...
1
vote
3answers
160 views

Prove without Parallel Postulate

Let x and y be parallel lines where x is not equal to y. How do I prove that y is in one of the 1/2 planes , let's call it H of x? How to prove that one of 1/2 planes of y is contained in H. Any ...
2
votes
0answers
460 views

Is it possible to use inversion to solve this USAMO problem in 2007?

I've no previous experience to solve any problems by inversive geometry but I am willing to see how it works. But I think I know some of the basic definition about inversion in geometry. Also I expect ...
1
vote
0answers
62 views

geometry of points in $\mathbf{Z^3} $ and center of mass

Given the set of $37$ points in $\mathbf{Z^3} $ in which no 4 points are on the same plane. Show that there exist 3 point A,B,C in this set such that $ (\frac{x_A+x_B+x_C}{3}, ...