Question

Learning outcomes
1. Students understand that the triangle and its shadow are similar.
2. Students verify the tests of similarity between the triangle and the shadow.
Remarks
1.
2.
3.
4.
Divide the class in small groups of 5 to 6 students. The number of groups will depend on
the class strength. Keep some set-ups ready, depending on the number of groups.
Instruct the students about the care they should take while handling the set-up so that the
triangle and its shadow are similar.
Tell the students to measure the lengths of sides of the triangle and its shadow. Find the
ratios of corresponding sides.
Take measure of all the angles of the triangle and the shadow. Make pairs of the
corresponding angles and write their measures.
Explain the students which test of similarity is proved if the ratios of the corresponding
sides are equal.
Similarly, explain them which test of
similarity is proved if two or three pairs of
corresponding angles are congruent.
Similarly, instruct them to prove the
remaining tests. Write all the measures and
proofs on the observation sheet.
5.
6.
7.
1.
Write the corresponding components of AABC and APQR to verify the SSS test.
Write the corresponding components of AABC and APQR to verify the AA test.
Write the corresponding components of AABC and APQR to verify the SAS test.
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Answer 1

Answer:

This implies that

x2+2ax=4x−4a−13

or

x2+2ax−4x+4a+13=0

or

x2+(2a−4)x+(4a+13)=0

Since the equation has just one solution instead of the usual two distinct solutions, then the two solutions must be same i.e. discriminant = 0.

Hence we get that

(2a−4)2=4⋅1⋅(4a+13)

or

4a2−16a+16=16a+52

or

4a2−32a−36=0

or

a2−8a−9=0

or

(a−9)(a+1)=0

So the values of a are −1 and 9.