EDITED Triangle

7/30/2019 EDITED Triangle

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Introduction

Types of Triangle

Constructing Triangles

Exercises


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Total angle within a triangle is 180o xo

yo zox o + y o + z o = 180 o

Triangle characteristics (I)

o

o

Apex

Side

Base

h

o = Apex Angle

o = Base Angle

h= Height

Triangle characteristics (II)

Bisection

Line

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Right

Isosceles

Scalene

Equilateral

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Same sides length

xo

xo xo

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Has a perpendicular angle

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Same base angles

Same sides length

xo xo

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0

0

0

x y z

0 0

0x

z

y

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Specific Condition (I)

Specific Condition (II)

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Constructing a triangle given:

3 Sides

2 Sides & 1 Angle

2 Sides & 1 Base Angle

Base & 2 Base Angles

Perimeter & Side Ratios

a

Click

the button

b

c

d

e

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a b c

Given 3 side a, b and ca

bc

Draw side a. On the point P, draw an arc with side b.

Construct an arc cfrom Q.

Draw the lines PR and QR.

P

Q

R

Step 1

Step 2

Step 3

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a

b

Given two sides aand band an

included angle 0

0

Draw side aand construct the angle 0

b

Construct an arc with side bfrom Q intersecting

at R and R.

R

R

Draw the lines PR and QR .The triangle PQR is an

alternative to triangle PQR.

0

aP Q

Step 1

Step 2

Step 3

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a

00

Given the base a and base angles 0

and 0.

Draw side aand construct angle 0.

0 0

Construct angle 0 as to intersect at R

R

Draw the lines to PR and QR.

aP Q

Step 1

Step 2

Step 3

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Given perimeter PQ.

Side ratios is 4:6:3.

P

Q

Divide the line PQ into 4:6:3 ratios. Mark C and D.

Centered at C and D, construct arcs with ratio PC

and DQ intersecting at E.

Draw the lines CD, CE and DE.

P

Q

D

36

C

4

E

Step 1

Step 2

Step 3

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Hypotenuse, h

a

Given hypotenuse and side a

Draw and bisect the hypotenuse. Construct a semicircle.

Centered at P, construct an arc with radius a

intersecting at R.

Draw the lines PR and QR.

P Q

R

a

Step 1

Step 2

Step 3

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a

0

Given the base a, base angle 0

and apex angle 0.

Draw the base aand

construct the apex

angle 0. Construct a

perpendicular line at A.Construct angle 0 at B.

Bisect AB so as to interact at O. Centered at O, construct a

circle through A and B so as to intersect at C.

Draw the lines AC and BC.

A

aB

0

0

O

C

Step 1

Step 2

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h

a

Given the height h,

base a, and apex

angle

0.

Draw base aand construct

the apex angle 0.

Construct a perpendicular

line at A. Construct a

parallel line hfrom AB.

Bisect AB so as to interact at O. Centre at O, construct a

circle through A and B so as to intersect at C and C.

Draw the lines AC and BC. The triangle

ABC is an alternative to triangle ABC.

A B0

a

O

C C

h

h

Step 1

Step 2

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Draw middle line Aaand

divide into three parts.

Centre at a, construct an arc with

radius 1/3 Aaintersecting at x.

Centre at x, construct arc with radius 2/3 Bband at h, withradius2/3 Ccintersecting at D.

Centre at h, construct

an arc with radius 2/3

Bb. Extend line Dato

intersect at E. Draw the triangle ADE.

A

B

C

a

b

c

Given the 3 bisector lines of a

triangle.

Aa

1

2

3

h

1/32/3

1/3

B

C

b

c

2/3

x

2/3Bb

2/3

2/3Cc

D

2/3Bb

E

Step 1

Step 2

Step 3

Step 4Step 5

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1) Draw the triangle ABC given the perimeter 210mm and

side ratios a : b : cof 6:4:3.

2) An isosceles triangle ABC with AB = AC = 110mm and

angle BAC 750. Draw the triangle.

3) Draw the triangle CDE given the base 85mm, apex

angle 300 and base angle 67.50.

4) Draw a right triangle ABC with hypotenuse 135mm and

one side 67mm.

5) Draw a right triangle ABC given a semicircle withdiameter 120mm and arc ratio of 2:4.

See the answer..

See the answer..

See the answer..

See the answer..

See the answer..

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Divide the line PQ into 5:5:3 ratios. Mark A and B.

Centered at C and D, construct arcs with radii PC and DQ

intersecting at E.

Draw the lines CD, CE and DE.

P

Q

3

2

B

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A

5

E

Draw the triangle ABC given the perimeter 210mm and side ratios

a:b:cof 5:5:3.

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1


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An isosceles triangle ABC with AB = AC = 110mm and angle BAC

750. Draw the triangle.

3

2

1

A

750

110mm

B

110mm C

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Draw the triangle CDE

given the base 85mm,

apex angle 300 and

apex angle 67.50.

3

2

1

A 85mm B300

67.50

O

5

4

C

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3

2

1

Draw a right triangle ABC with hypotenuse 135mm and one

side 67mm.

P135mm

Q

67mm

R

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3

2

1

Draw a right triangle ABC given a semicircle with diameter 120mm

and arc ratio of 2:4

A

120mm B

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