Download WORK SHEET 4(2 Term)

WORK SHEET 4(2nd Term)
Session: 2014-15
Name:___________________________________________ Class: VII Sec:_______________ Roll:_____
Sub: Geometry
Teacher: Sarwat Sultana
Date:____________________________
Week: 22.02.2015(Sunday) to 26.02.2015(Thursday)
Assalamu Alaikum, students. Today we have our immortal ‘Ekushey February’ – Our Shaheed Dibash
(Martyrs’ Day). This day, we, in black and white, murmuring songs of lament, visit Shaheed Minar to pay our
homage to the language martyrs.
And this week we shall learn more about Similarity. Similarity & Shaheed Dibash! Any link between these
two? Yes! Look at the monument – the Shaheed Minar all over the country. Aren’t they all similar? The same
shape but of different sizes.  Therefore, what is similarity in Geometry?
DAY 1 (SUNDAY): Read thoroughly the following notes on Similarity &Similar figures:
Two geometrical objects are called similar if they both have the same shape, or one has the same shape as the
mirror image of the other. For example, all circles are similar to each other, all squares are similar to each other,
and all equilateral triangles are similar to each other. On the other hand, ellipses are not all similar to each other,
rectangles are not all similar to each other, and isosceles triangles are not all similar to each other.
Similar Triangles (Angles, Sides & Similarity Ratio): What are similar triangles? Similar triangles have the
same 'shape' but are just scaled differently. Similar triangles have congruent angles and proportional sides.
[Notation: △ABC~△XYZ means that "△ABC is similar to △XYZ"]
How to Tell if Triangles Are Similar :To find if triangles that are similar we must compare corresponding sides
and/ or corresponding angles. Now, how to find corresponding sides. Corresponding sides follow the same letter
order as the triangle name so. The example below shows corresponding sides and corresponding angles.
AB of ΔABC and DE of ΔDEF are corresponding sides
BC of ΔABC and EF of ΔDEF are corresponding sides
CA of ΔABC and FD of ΔDEF are corresponding sides
∠BAC of ΔABC and ∠EDF of ΔDEF are corresponding angles
∠ACB of ΔABC and ∠DFE of ΔDEF are corresponding angles
∠CBA of ΔABC and ∠FED of ΔDEF are corresponding angles
There are several combinations of conditions that show whether two triangles to be similar.
1) If two pairs of the corresponding angles are equal then the triangles are similar. That is, in the above
figure, if ∠BAC = ∠EDF, ∠ACB = ∠DFE, and ∠CBA = ∠FED then ΔABC is similar to ΔDEF.
2) If all three pairs of corresponding sides are in the same ratio (proportional) then the triangles are
AB BC AC
similar. That is, in the above figure, if


then ΔABC is similar to ΔDEFatio) is
DE EF DF
There are several elementary results concerning similar triangles:
 Any two equilateral triangles are similar.
 Two triangles, both similar to a third triangle, are similar to each other .
 Corresponding altitudes of similar triangles have the same ratio as the corresponding sides.
 Two right triangles are similar if the hypotenuse and one other side have lengths in the same ratio.
Two points to note for triangles:
1) If two pairs of corresponding angles are equal then the third pair will always be equal too (since the sum
of the three angles in a triangle is always 180°).
2) If one set of the conditions (e.g. corresponding sides in the same ratio) is true then the other set (e.g.
corresponding angles being equal) is also true.
Other Similar Polygons
 The concept of similarity can be applied for other polygons as well as triangles.
 Given any two similar polygons, corresponding sides taken in the same sequence (even if clockwise for
one polygon and counterclockwise for the other) are proportional and corresponding angles taken in the
same sequence are equal.
 Other than triangles, to tell if the polygons are similar, both the properties of similarity are required.
That is, only proportionality of corresponding sides (otherwise, for example, all rhombi would be
similar) or equality of all angles in sequence, (otherwise all rectangles would be similar) is not sufficient
to guarantee similarity.
 A sufficient condition for similarity of polygons is that corresponding sides and diagonals are
proportional.
DAY 2 (TUESDAY): Check your progress. Practice the following problems dealing with similar figures.
1) Which of the following triangles are always similar? Give reason for your answer.
a. right triangles
b. isosceles triangles
c. equilateral triangles
2) The sides of a triangle are 5, 6 and 10. Find the length of the longest side of a similar triangle whose shortest
side is 15.
3) Given: In the diagram, DE is parallel to AC, BD = 4, DA = 6 and EC = 8.
a) Prove ΔABC is similar to ΔDBE [Hint: with reasons, show any two pairs of
corresponding angles are equal]
AB BC AC
b) Find BC to the nearest tenth. [Hint: similar triangles :


]
DB BE DE
4) Construct any triangle of any measure with ruler and pencil.
a) Measure the angles and sides of the triangle.
b) Construct another triangle similar to the first one.
[Hint: Construct equal angles and proportional sides with your own similarity ratio]
Tear here
HOME WORK 4(2nd Term)
Session: 2014-15
Name:___________________________________________ Class: VII Sec:_______________ Roll:_____
Sub: Geometry
Teacher: Sarwat Sultana
Date of Submission:27.02.2015(Friday)
Do the H.W. on loose sheet. Staple this worksheet on top of your H.W.
1) Two triangles are similar. The sides of the first triangle are 7, 9, and 11. The smallest
side of the second triangle is 21. Find the perimeter of the second triangle.
2) Using the figure at right, prove ΔABC is similar to ΔDBE and find the length of BC.
3) Two ladders are leaned against a wall, such that they make the same angle with the
ground.
a) The 10 feet ladder reaches 8 feet up the wall. How much further up the wall
does the 18 feet ladder reach?
b) Find the distance between two ladders on the ground.
[Hint: Apply Pythagoras to get distances from the ladders on the ground to the
foot of the wall.]
[Remember, diagram is a MUST for every sum.]