NEW MILLENNIUM ACADEMY
Geometry Worksheet
Specification Grid
| Level | Questions | Marks Breakdown | Total Marks |
|---|---|---|---|
| Knowledge (K) | 2 | 1 + 1 = 2 | 2 |
| Understanding (U) | 2 | 2 + 2 = 4 | 4 |
| Application (A) | 2 | 3 + 3 = 6 | 6 |
| Higher Ability (HA) | 2 | 2 + 1 = 3 | 3 |
| Total Questions: 8 | - | Total Marks: 15 | |
Set - 1
Questions 1-3
Q.N. 1: Teacher made a geometric figure to test students' knowledges on pairs of angles.
a) Write an alternate angle of \(\angle BFG\). [1K]
b) Make a table and show interior and exterior angles formed by transversal \(EH\) with pair of lines \(AB\) and \(CD\). [2U]
c) If \(\angle EFB = 2a + 15^\circ\) and \(\angle FGD = a - 10^\circ\); for what value of '\(a\)' the lines \(AB\) and \(CD\) will be parallel lines. [2HA]
Q.N. 2: Radhika was told to draw three triangles on her copy. She drew as follows:
fig-I
fig-II
fig-III
a) What is the measurement of each angles in figure III? [1K]
b) Copy and complete the table: [3A]
| fig | \(\angle A\) | \(\angle B\) | \(\angle C\) | \(\angle A\) + \(\angle B\) + \(\angle C\) | Result |
|---|---|---|---|---|---|
| I | |||||
| II | |||||
| III |
c) Janaki says,"The sum of three angles of all triangles many not be equal to 2 right angles". Is she correct? Write your own conclusion. [1HA]
Q.N. 3: Sarthak wants to challenge Biroj by giving a figure based question as shown in figure.
a) Calculate the numberic value of '\(x\)' with reason. [2U]
b) Prove that: \(\triangle ABC\) is an isosceles triangle. [3A]
Set - 2
Questions 1-3
Q.N. 1: A mathematics teacher showed a geometric figure to check students' understanding on angle pairs.
a) Write a pair of co-interior angles from given figure. [1K]
b) Find the value of '\(b\)' with geometric reason. [2U]
c) What must be the measurement of angle \(\angle GJI\) so that lines \(JI\) and \(GH\) will be parallel? Explain. [2HA]
Q.N. 2: Priya drew three triangles in her notebook as follows:
fig-I
fig-II
fig-III
a) What type of triangle is \(\triangle ABC\) having two sides equal? Write. [1K]
b) Copy and complete the table: [3A]
| fig | \(\angle A\) | \(\angle B\) | \(\angle C\) | Result |
|---|---|---|---|---|
| I | ||||
| II | ||||
| III |
c) What conclusion can be drawn from the result of above table? [1HA]
Q.N. 3: There was a figure based question asked in BEE of one muncipality maths' exam:
a) Calculate the numeric value of '\(a\)' with geometric reason. [2U]
b) Prove that: AB and CE are parallel lines, if the ratio of \(\angle ACE\) and \(\angle ECD\) is 6:7. [3A]
Set - 3
Questions 1-3
Q.N. 1: During board test in class-8, teacher draw the given figure:
a) Write a pair of corresponding angles from given figure. [1K]
b) Find the value of '\(m\)' with geometric reason. [2U]
c) What must be the measurement of angle \(\angle GDF\) so that lines \(GE\) and \(DF\) will be parallel? Explain. [2HA]
Q.N. 2: Anjana was told to draw three triangles on her notebook copy. She drew as follows:
fig-I
fig - II
fig-III
a) Write the measurement of each interior angle of an equilateral triangle. [1K]
b) Copy this table and complete it: [3A]
| fig | \(\angle A\) | \(\angle B\) | \(\angle C\) | Result |
|---|---|---|---|---|
| I | ||||
| II | ||||
| III |
c) Sita says, "If the base angles of an isosceles triangle is \(60^\circ\) then obviously it is an equilateral triangle". Is she correct? Justify. [1HA]
Q.N. 3: Maya's father asked his daughter to draw a geometric figure with parallel lines and triangle. Mean while Maya drew the figure as shown:
a) Calculate the numeric value of '\(y\)' with reasons. [2U]
b) Prove that: \(\Delta PQR\) is an isosceles triangle. [3A]
Set - 4
Questions 1-3
Q.N. 1: Study the given figure with parallel lines and transversal.
a) Write a pair of alternate angles from given figure. [1K]
b) Find the value of '\(a\)' with geometric reason. [2U]
c) Sita says, "\(\angle EFB\) and \(\angle DGH\) are equal." Gita says, "\(\angle EFB\) and \(\angle CGH\) are equal." Who is correct? Justify. [2HA]
Q.N. 2: Rasika drew these three triangles in her note copy.
fig-I
fig-II
fig-III
a) Write the sum of acute angles of a right angled triangle. [1K]
b) Copy and complete the table: [3A]
| fig | \(\angle A\) | \(\angle B\) | \(\angle C\) | Result |
|---|---|---|---|---|
| I | ||||
| II | ||||
| III |
c) What conclusion can be brought out from given the result of above table? [1HA]
Q.N. 3: Answer the following sub-questions based on the given diagrams:
a) Find the value of '\(a\)' from given figure: [2U]
b) From the given figure, prove that \(\Delta ECD\) is an equilateral triangle. [3A]
Set - 5
Questions 1-3
Q.N. 1: Rijal sir thought for a while and started drawing the given geometric figure.
a) Write a pair of corresponding angles from given figure. [1K]
b) Find the value of '\(x\)' from given figure. [2U]
c) What must be the measurement of \(\angle CBF\) so that lines \(AE\) and \(BF\) will be parallel? [2HA]
Q.N. 2: Work out the triangle properties based questions:
a) Verify experimentally, "Sum of angles of a triangle is two right angles". [3A]
b) Write one similarity and one difference between isosceles triangle and an equilateral triangle. [2U]
Q.N. 3: Evaluate geometric systems and numerical values:
a) Write the relation between lines \(AB\) and \(CD\). [1K]
b) In \(\Delta ABC\), \(3\angle A = 2\angle B = 6\angle C\), prove that: \(\Delta ABC\) is a right angled triangle. [3A]
c) These sets contains angles of different triangles.
\(S_1 = \{90^\circ, 60^\circ, 30^\circ\}\)
\(S_2 = \{60^\circ, 60^\circ, 60^\circ\}\)
\(S_3 = \{48^\circ, 100^\circ, 36^\circ\}\)
\(S_4 = \{63^\circ, 37^\circ, 80^\circ\}\)
\(S_5 = \{55^\circ, 65^\circ, 60^\circ\}\)
In which set measurement of angles is written incorrectly? Why? [1HA]
\(S_1 = \{90^\circ, 60^\circ, 30^\circ\}\)
\(S_2 = \{60^\circ, 60^\circ, 60^\circ\}\)
\(S_3 = \{48^\circ, 100^\circ, 36^\circ\}\)
\(S_4 = \{63^\circ, 37^\circ, 80^\circ\}\)
\(S_5 = \{55^\circ, 65^\circ, 60^\circ\}\)
In which set measurement of angles is written incorrectly? Why? [1HA]