I have some tough geometry questions I need the answers of urgently. Read on...?

Question

1. Prove that any straight line drawn to form the vertex of a triangle to the base is bisected by the straight line that joins the midpoints of the other sides.

2. AD and BE are the altitudes of an isoscles triangle ABC with AB = BC. Prove that AE = BD

3. In a triangle ABC, the bisector of angle A meets base BC at D. Prove that AB>BD

4. In a triangle PQR, S is any point on QR. Prove that PQ + QR + PR > 2PS

5. If two isosceles triangles have a common base, then prove that the line joining their vertices bisects them at right angles.

6. In triangle ABC, D is the midpoint of AB and P is any point on BC. A line CQ is drawn parallel to PD to meet AB at Q.
Prove that ar(BPQ) = 1/2 ar(ABC)

Can anyone answer something other than the first one?

Answer 1

Your first Question:

Now,

Imagine a Triangle with vertices ABC.
Any line from A to BC is AD. D is the point of intersection on BC.

Let E and F be the midpoints of Sides AB anc AC respectively.

Join E and F to meet AD in G.

Now for the proof:
Take Triangles AGE and ADB these two are similar.

Reason being that EF would be parallel to BC from Mid Point theorem. Therefore, the two triangles will be similar as Angle E and Angle B are equal and Angle A is common.

Now take Triangle ADB, E is the mid point of AB and EG is parallel to BD there for from Converse of Midpoint Theorem G becomes the Midpoint of AD.

Hence proved.

Answer 2

1.let ABC be the triangle and let AD be any line from vertex A onto D,a point on BC
letEF be the line joiningthe midpoints of AB and AC respectively.
To Prove that AD is bisected by EF
let the point of intersection of AD and EF be G
To Prove that AG=GD
line EF parallel to line BC (midpoint theorem)
draw XY parallel to EF and hence BC through A
now the parallel lines XY,EF and BC make equal intercepts AE and ED on transversal AB
so by intercepts theorem they must make equal intercepts on AD also
soAG=GD
hence proved

i have done one for you
transversal

Answer 3

sure. that's referred to as Divine Laziness, and Ignorant layout. Ignorant layout comes into it even as human beings answer a thoroughly distinct question to what became requested, or pick to rant truly of answering. a outstanding get mutually I once had became a shrink'n'paste that crammed the web page, yet did not answer the question in any respect. i have also had some those who thoroughly forget with regard to the question itself, and purely say stuff like 'I agree'. ok, you agree. truthful adequate, now would you pick to inform me your answer at any time? Divine Laziness is the different large non secular clarification for no longer interpreting. It takes the kind of a question format (i will thieve your get mutually): Q: Why do not Xs ever seem to tolerate Ys? QD: i do not in my opinion imagine there is many Xs who dislike Ys, that's only a small minority who tend to be truly rude and disgusting of their attitudes. A case of the noisiest few, to be able to communicate. what's your opinion in this? A: we are no longer ALL like that!!! provide up being so judgemental!! ummmm.....study IT next TIME!!!! lol. ((((hugs))))

Answer 4

1. By equal intercept theorem,If any 3 lines are drawn parallel to each other, the intercepts made by any 2 or more intercepts are equal and in the same line , they are proportional.
Using this theorem, we can prove the first prob.

Answer 5

______________/when it riches the line.

AD+BE=16 B because this answer as known be Hex..

A angel can't connect together 2-4 points of angels. AB>BD=C

PQ+PR+QR: SPRQ connect together.

i know this:it becomes like a dormer

And P can't be connect if near each other

Answer 6

These are the theorems and corollary of them. U can find the proof in some good trigonometry book with detailed explanation.