Calculate with reasons, the size of the unknown angles. Greek symbols or lower case letters.
Triangles : Based on an angles.
Traingles : Based on the sides
Exercise
Identify the types of triangles given below ( Based on angles)
Identify the types of triangles given below ( Based on sides)
Solutions:
Example
Writing method.
Exercise
Find the missing angles in the following triangles.
Exercise
Find the missing angles in the following triangles.
Example
Exercise
Example :
Exercise:
a. Calculate, with reasons, the value of x in each of the following example and then find the value of each angle.
b. Calculate, with reasons :
Solutions:
Types of Quadrilaterals.
There are Three special types of parallelograms.
Properties of quadrilaterals.
Note : Total of all interior angle of any quadrilateral is 360.
Examples
a.
ABCD is a parrllelogram. Calculate, with reasons, the unknown angles marked with x and y.
NOTE : Parallelogram will be also called as "Parm" an abbreviation.
b.
ABCD is Parm. AD=DQ=QC=AQ and AQ is 5
Calculate, with reasons, sides of parm ABCD.
C.
d.
Exercise
a.
b.
Examples:
a.
Solution:
b.
Exercise:
1.
2.
3.
4.
5
6.
7.
8.
9.
Solutions:
Congruent shapes:
Congruency in Triangles : ( Most Important )
1.
AB = PQ ( 4 cm given)
BC = QR (3 cm given )
AC = PR (5 cm given)
2.
AB = DF ( 13 cm given)
AC = FE ( 5 cm given)
CB = DE ( 12 cm given)
3.
MN = PQ ( given)
NO = QR ( given)
OM = RP ( given )
4.
NO = QR ( given)
OM = RP ( given )
Writing method of congruent triangles ( Very Important )
Examples :
1. Concentrate on the following diagrams. Prove that triangles are congruent. Use proper symbols of congruency.
2. WXYZ is a rectangle. Identify and Prove the triangles which are congruent. Use proper symbols of congruency.
STEP 1 : Breakdown rectangle into two triangles and arrange them so that we can see same type of indication.
Step 2 : Compare angles and sides by providing reasons.
Exercise :
Use you understanding of congruency to prove the two triangles are congruent.
a.
b.
c.
d. ABCD is rectangle.
e.
f.
g.
h.
I. ABCD is a square. Show that two triangles are congruent.
j. ABCD is rhombus.
K. PQRS is kite. Show that two triangles are congruent.
l. ABCD is parallelogram and AECF is rectangle. Show that two triangles (AFD and CEB) are congruent.
Solutions:
Shapes
Examples:
a.
b.
