# Tagged Questions

81 views

### Construction of an equilateral triangle from two equilateral triangles with a shared vertex

Problem Given that $\triangle ABC$ and $\triangle CDE$ are both equilateral triangles. Connect $AE$, $BE$ to get segments, take the midpoint of $BE$ as $O$, connect $AO$ and extend $AO$ to $F$ where ...
33 views

### How prove that $|QA| < |QC|$ in triangle?

$ABC$ is a triangle with a right angle at $A$, and $|AB|$ > $|AC|$. The point $D$ is defined so that $BCD$ is equlateral and $AD$ intersects $BC$ at $P$. The point $Q$ is defined so that $QDP$ is ...
77 views

### How show that $ABC$ is equilateral?

Let $D$, $E$ and $F$ be three points on sides $BC$,$AC$ and $AB$ of triangle $ABC$ such that lines $AD$, $BE$ and $CF$ concur at point $M$. If three trianles $MDB$, $MCE$ and $MAF$ have equal areas ...
43 views

### How prove that $AD>BE$ in triangle?

Let $D$ be a point on the side $BC$ of a triangle $ABC$ such that $AD>BC$ . The point $E$ on $CA$ is defined by the equation $\frac{AE}{EC}=\frac{BD}{AD-BC}$ .How prove that $AD>BE$?
168 views

### 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 ...
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 ...
57 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 ...
59 views

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 $S$, ...
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 ...
37 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 ...
55 views

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 ...
94 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 ...
133 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:)
206 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 ...
146 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 $E$. ...
79 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 ...
94 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 ...
65 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 ...
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 ...
117 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 ...
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 ...
307 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, $AB > AD$ ...
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 ...
272 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 ...