Triangle

GOVT. GIRLS HIGH SCHOOL PAYAL PROJECT NAME: CONSTRUCTION & PROPERTIES OF TRIANGLE STUDENT’S NAME: NEETU JOSHI JASVIR KAUR LOVEJEET KAUR GUIDANCE WITH- Smt. HARPREET KAUR (MATH MISTRESS)

Triangle A figure has three sides is called a Triangle. Symbol “ Δ “ is used for a Triangle.

Triangle

Construction

Properties

Construction of a triangle when its two sides and an angle between them are given . • • 3. 4. 5.

Yc m

Given :- PR=x cm PQ=y cm and P=Q Construction:Draw a line segment PR = x cm. Construct
X cm

R

Construction of a triangle when its two angles and one side between them are given. • • 3. 4. 5. 6.

Given :-
X

β

α A

X cm

B

Construction of a triangle when its there sides are given. • • 3. 4. 5.

Z

Given:- AB=x cm, BC=y cm, AC=z cm Steps of construction :Draw a line segment BC = y cm Let B as a center, draw an arc of radius x cm Let C as a center, draw an arc of radius z cm that cut the previous arc, at point A 4. Join A and B A 5. Join A and C m c X Then, Δ ABC is the required triangle cm

B

Y cm

C

Construction of a triangle when it’s Base, sum of other two sides and one Base angle are given.

Y

cm

D

x

• Given:- Base BC=a cm, AB+AC=x cm &
L

a cm

C

X

Construction of a triangle when it’s Base, difference of other two sides and one Base angle are given.

p

Y

A

d

cm

• Given:- Base BC = a cm, AB-AC = d cm and
C

X

Construction of a triangle of a given perimeter and base angles . •

Given: Perimeter AB+BC+CA=x cm,
β/2`

α/2 B X C.M.

C

N

X

Construction of a triangle whose two sides and a median corresponding to one of these sides are given. • Given: AB=x cm, BC=A cm, Median CD=d cm • Steps of construction: 1. Draw a line segment AB=x cm. 2. Bisect AB . Let D be its mid-point . 3. With D as centre and radius d cm, draw an arc. . 4. With B as centre and radius a cm, draw another ac

m

d cm

arc, intersecting the above arc at a point C. 5. Join CB and CA. Then , ΔABC is the required triangle. A

C

x cm

D

B

Construction of a triangle equal in area to a given quadrilateral. • Given: A quadrilateral ABCD. • Steps of Construction: 1. Join A and C. 2. Through D, draw a line segment DE, parallel to AC intersecting BC produced at a point E. 3. Join A and E. D Then , ΔABE is the required A triangle.

B

C

E

Construction of a right angle triangle when its hypotenuse and one side are given Given: EF=x cm, DF=y cm, <E=900 Steps of construction: 1. Draw a line segment EF=x cm. 2. Construct <XEF=900 3. Let F as a center, draw an arc of radius Y cm, that cut the ray EX, at a point D. X 4. Join D & F. D Then , ΔDEF is the required triangle.

yc m

900 E

X cm

F

Properties of Triangle 1. 2. 3. 4.

The sum of three angles of a triangle is 1800. Interior angle is equal to the sum of opposite interior angle. The sum of two sides of a triangle is greater than the third side. If two sides of a triangle are equal then there opposite angles are also equal. 5. If three sides of a triangle are equal then three angles of triangles are also equal. 6. If two angles in a triangle are equal then the two sides are also equal. 7. In right angle triangle sum of square of two sides is equal to the square of third side. 8. If the square of one side is equal to the sum of square of other two sides then the two sides are equal. 9. There are three medians of a triangle from three vertex. 10. There are three perpendiculars of a triangle from three vertex. 11. If we want to find centre of triangle we draw two perpendicular bisector.