2.4 Similarity

Homework assignment

1. The following pairs of triangles are given. State whether they are similar or not and give reasons for you answer. If the two triangles are similar, calculate the lengths of the sides not given and also the magnitudes of the angles not given in the figure.

Example:

C = F = 60°Δ ABC  ΔEDF ()

AB = 4 cmAC = 5 cm (pyth)EF = 10 cm

1.1.

1.2

1.3.

1.4

2.

2.1 Complete the following:

In ΔAOB and ΔDOE:

Re a son

.......... = .......... (...........................................................................)

.......... = .......... (...........................................................................)

Δ.............. .............. ( )

2.2 Now calculate the lengths of the sides not given in the figure.

3.

3.1 Complete the following:

In Δ.......... and Δ..........

.......... = .......... (...........................................................................)

.......... = .......... (...........................................................................)

Δ.............. .............. ( )

3.2 Calculate the lengths of the following:

3.2.1 HE

3.2.2 EG

3.2.3 FJ

4. The height of a high vertical object can be determined by measuring the length of the shadow of a stick of known length and the shadow of the object. The following figures give the measurements which were made.

Determine the length of the flagpole.

ASSESSMENT TASK:

To use similarity to calculate the height of an object:

• Work together in pairs.

1. The following are needed:

• A measuring tape of at least 5 m
• A mirror
• A ruler
• A Koki pen

2. You do the following:

• Look for two high vertical objects on the school grounds; for e x ample a netball pole, a lamp pole, rugby poles or a flagpole. Look for objects of which the heights are normally difficult to measure using normal methods.
• Draw two thin lines on the mirror using the Koki pen so that the lines are perpendicular to each other.
• Place the mirror a distance from the object on level ground.
• One person should then step back and look in the mirror and change his / her position until the top of the object is precisely on the point of intersection of the two lines in the mirror.

3. Measure the following:

• the height of the eyes above the ground of the person who looked in the mirror;
• the distance between the person who looked in the mirror and the point of intersection of the lines in the mirror’
• the distance between the object and the point of intersection of the lines in the mirror.

Results:

1. Copy the table on folio paper and complete it:

2.

PKSLV

In the sketch PK is the height of the eyes of the person, S is the position of the mirror and VL is the height of the object, which is measured. Explain why ΔPKS  ΔVLS.

3. In this task the measurements can be inaccurate. Explain which mistakes could have been made, which could influence the accuracy of the height of the object measured.

Assessment