Problem: a, b, c are lengths of side of a triangle

Let a, b, c are lengths of three sides of a triangle, and:

Show that: P < 0

Solution:

We can assume that c this the longest side of the triangle ABC (it does not make different if the longest side is a or b), draw the height CH with H is on AB => H is lying between points A and B (see the pic below)

then: 

let change the expression P as following:

Geometry problem (2)

Given triangle ABC, angle BAC < 90 degrees. Two squares with side AB, AC are drawn outside of the triangle. M is a midpoint of BC. Show that DM ⊥ ME and DM = ME

Geometry Problems (1): Prove that points are laying on one circle!

Given arbitrary five-wings star, the circumscribed circles of its wings are drawn. Show that intersections points A, B, C, D, E are laying on one circle!

Geometry Pad-2D: Select an object to work with

In many cases you need to select an object (point, line segment, circle, triangle, polygon, angle) to work with. For example, you want to draw a circumscribed circle of triangle ABC, in this case you need to select triangle, and use triangle tools to draw its circumscribed circle.

There are some ways to select an object in the construction showing in screen:

Select by tapping on screen

• To select a point, you can simply tap nearly it on screen
• To select a line segment: tap nearly its center point
• To select a circle: tap on it
• To select a triangle, polygon: tap somewhere in the "centre" of a shape
• To select an angle: select its vertex first, then tap somewhere inside its, nearly but not too close to the vertex     

select an object by tapping on screen

Limitation: when your construction is complex enough, this may make some confuse when you tap on the screen. For example, when two or more line segments have the same center point or there are some angles with the same vertex,...

Note: the selected object by default will be highlighted light-green filling

Use "bottom" tools 

This tools will appeared when you select some point. It is to help you select objects related to the selected point. For example, when you select point "B", the "line segment" selection tool will show you all line segments comes from/to point "B".

bottom selection tools

Limitation: this method shows you all possible variations for choosing an objects, sometime there are too many variations and it makes you difficult to detect which one is your object!

Use main selection tools

This is the most careful method to select an object, it was designed for line segments, triangles, angles and polygons. Steps to choose an object are:

1. Choose selection tool
2. Choose type of object
3. Tap on all points (vertices) of an object which you want to select

Note: You should tap on the points in order you needed. For example, when you tap points: "A", "B", "C", angle ABC will be selected; but tapping on "B", "A", "C" will select angle "BAC". In the case of polygon: quadrilaterals ABCD and ACBD are different each of other!

Free download

2014.11.13
Geometry 2D-Pad on Facebook

Geometry Pad-2D: Working with triangle [1]

Suppose that we have some problem like: "Given triangle ABC with the height AH, draw line HD // AC, D is on side AC...."

pic 1

With the "Geometry Pad-2D" app, you can draw the picture easily by following steps:

Step 1: Draw triangle ABC

Step 1: Draw triangle ABC

a) Tap on the "+" tool of the TOP toolsbox
b) Tap on the "triangle" tool of the RIGHT toolsbox
c) Select type of triangle
d) Move triangle into right position 

Note: You also can change the drawn triangle by tap on any vertex or side then move it, change it using points or line segments tools

Step 2: Draw height AH

There are different ways to draw the heights of triangle: use points tools, use lines tools or use triangle tools. The following shows how to use points tools to draw height AH.

a) Select vertex A
b) Select "draw perpendicular segment" tool
c) Select showed point to draw line to...

Note: new the point on BC is automatically named as "D", we will change name of the point later.

Step 2: Draw height from A

Step 3: Draw line segment parallel to  AB

a) Select line AB, then select point D
b) Select "draw perpendicular..." of the Right toolsbox
c) Tap on small brown circle appeared on AC

Step 3: Draw DE // AB

Note: by default, new added line segments have "dotted" style









Step 4: Naming, styles and colours

a) Now you can use points tools (select any point to show point tools on the right side of screen) to change name(s) of points. In our case change "D" -> "H" and "E" -> "D"

(The naming tool is the first one of the points toolsbox)

b) Select line segment to show lines toolsbox on the right side of screen. Use change line-style, change line-colour tools to make a picture look as you want

line segments toolsbox

c) Select angle AHC and mark it with, the right angle mark will be drawn

mark angle

Free download

2014.11.10
Geometry 2D-Pad on Facebook

Geometry 2D-Pad: How to add new object?

Free download

This is to describe the first way to add new object to a geometry construction using Geometry 2D-Pad (v2.0) on your iPad (with iOS 7++). In our example, the new object is a triangle.

1) Tap the "add" tool on the top screen menu (+)
2) Tap the triangle tool on the right toolset (it appeared after 1st action)
3) The new triangle with the "moving circle" (pink) will appeared in drawing screen
4) Drag and drop the new shape with the pink circle at the right position

See the picture:

Step to add new triangle

The triangle ABC has been added. Now you can choose it and use "working with triangle toolset" to add the altitude AH as bellow:

Choose triangle ABC and draw altitude AH

Notes: before moving the new triangle, you could see some interesting pictures on the bottom side of drawing area, what is it? This is a new interesting feature, which allows you to choose a type of new triangle: equilateral, right or isosceles. Let try it and see the results!

It is so easy, isn't it?

Free download

2014.10.03
Geometry 2D-Pad on Facebook

How to draw an inscribed and a circumscribed circles of a triangle?

(O1) is an inscribed, (O2) is a circumscribed circle of triangle ABC

This post is to show how to use Geometry Drawer tools to draw an inscribed and a circumscribed circle of a given triangle. On a paper, this task is a combination of several activities to detect a centre points of required circles. With Geometry Drawer Tools it made easy:

1) Select a triangle ABC with selection tools or by selecting point A, then long press on on side BC
2) When the triangle is selected, the circles tools will be appeared.
3) Select required tool and drag it into drawing area, then drop it

That is all! See the picture bellow:

Tools for drawing an inscribed and a circumscribed circles

Notes:

1) The picture is taken by Geometry Drawer for iPhone. It is the same way for drawing by Geometry Drawer for iPad.

2) After the above task, you can use circles tools to change style and colour of a drawn circles

11.6.2014

Geometry Drawer on Facebook

Plane Geometry Drawer for iPhone