# Elementary geometry questions and answers

Recent questions in Elementary geometry
Davian Lawson 2022-05-02

### In a triangle ABC, the interior cevian CM is drawn, so that $CM=AB$ ; Knowing that the measure of $\mathrm{\angle }A=30°$ and $\mathrm{\angle }B=100°$ . Calculate the measure of $\mathrm{\angle }MCB$ .

Bruce Rosario 2022-04-30

### The hopf map in terms of quaternions is defined as$h:r↦{R}_{r}\left({P}_{0}\right)=ri\overline{r}$where r is a unit quaternion and ${P}_{0}=\left(1,0,0\right)$ is a fixed point. If a point $r\in {S}^{3}$ is sent by the Hopf map to the point $P\in {S}^{2}$ , a formula can be derived for a particular representation for the cosets. In my case, I want to derive a formula for the ${180}^{\circ }$ rotations around an axes through i and other points in ${S}^{3}$ .

windpipe33u 2022-04-30

### This may be a dumb question.The Poisson postulates are:1. $P\left(n=1,h\right)=\lambda h+o\left(h\right)$2. $\sum _{i=2}^{\mathrm{\infty }}P\left(n=i,h\right)=o\left(h\right)$3. Events in nonoverlapping intervals are independentWhat ensures that $\lambda h\in \left[0,1\right]$ irrespective of the value of $\lambda$ ?

albusgks 2022-04-30

### If a line L separates a parallelogram into two regions of equal areas, then L contains the point of intersection of the diagonals of the parallelogram.The figure shows a line L horizontally through the sides of the parallelogram.This creates two trapezoids and I can intuitively show that if the bases of the trapezoids are not congruent then the areas can not be equal.I just can not currently see how to relate the intersection with the diagonals.Any help will be appreciated.

vacinammo288 2022-04-30

### I've been away from math far too long, and now my memory plays tricks on me when I try to recall simple facts.I know that $det\left({v}_{1},\dots ,{v}_{n}\right)$ is the oriented volume of the simplex determined by the origin and the vectors ${v}_{1},\dots ,{v}_{n}$ (up to a constant factor depending on the dimension $n$).But I fell into utter confusion when I tried to make up why, especially when I tried to prove that this formula works for a shifted simplex, too.What I'm sure is that det is an alternating bi-linear form that fits naturally with an oriented volume function.What I've found on the net is dependent on what definition is used, and prone to circular reasoning.Explicit question: how and why is the oriented volume of a simplex related to the determinant of its vectors?What I've tried: proved it for $n=1,n=2,n=3$, and I've seen that this is not the way to go.

Oberhangaps5z 2022-04-07

### If ABCD is a parallelogram and point M is the midpoint of AB then in what ratio does the intersection of diagonal AC and the straight line DM split AC?

Ashley Fritz 2022-04-07

### Consider the triangle $\mathrm{\Delta }ABC$ , which D is the midpoint of segment BC, and let the point G be defined such that $\left(GD\right)=\frac{1}{3}\left(AD\right)$ . Assuming that ${z}_{A},{z}_{B},{z}_{C}$ are the complex numbers representing the points (A, B, C):a. Find the complex number ${z}_{G}$ that represents the point Gb. Show that $\left(CG\right)=\frac{2}{3}\left(CF\right)$ and that F is the midpoint of the segment (AB)

vilitatelp014 2022-04-07

### We have a $\mathrm{△}ABC$ and a $\mathrm{△}{A}_{1}{B}_{1}{C}_{1}$. The segments $CL$ and ${C}_{1}{L}_{1}$ are angle bisectors. If $\mathrm{△}ALC\sim \mathrm{△}{A}_{1}{L}_{1}{C}_{1}$, I should show that $\mathrm{△}ABC\sim \mathrm{△}{A}_{1}{B}_{1}{C}_{1}$.From the similarity, we have $\frac{AL}{{A}_{1}{L}_{1}}=\frac{CL}{{C}_{1}{L}_{1}}=\frac{AC}{{A}_{1}{C}_{1}}$. The only way I see from here is to show that $\mathrm{△}LBC\sim \mathrm{△}{L}_{1}{B}_{1}{C}_{1}$. Is this necessary for the solution?

Bernard Mora 2022-04-07

### 1) I know that all inner product space is also a normed space with the norm induce by the scalar product, but is the reciprocal true ? I mean, is all normed space also a inner product space ?2) I know that all normed space is a metric space with the metric induced by the norm. Is the reciprocal true ? I mean, is all metric space also a normed space ?

Elle Weber 2022-04-07

### The formula for local midpoint rule in the interval

indimiamimactjcf 2022-04-07

### Given the endpoints (11, 23) and (6, 13) of a circle, find the equation of the circle and the equation of a line tangent to the circle.

velinariojepvg 2022-04-06

### Find the distance from the origin to the point (7, 4).I know that I have to use the formula for the length of a line and midpoint but I am unsure of what the question is asking.

Jordon Haley 2022-04-06

### What term/identity/theorem states that given a triangle the largest angle must be opposite the longest side?

hyprkathknmk 2022-04-06