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Triangles

Short Answer Type

171. In the figure given below, ABCD is a quadrilateral with AC = AD and AB bisects ∠A. Show that ∆ABC ≅ ∆ABD. What can you say about BC and BD?

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172.

In figure, AB ⊥ AE, BC ⊥ AB, CE = DE and ∠AED = 120°. Find
(a)     ∠EDC
(b)     ∠DEC
(c)    Hence prove that EDC is an equilateral triangle.

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Fill In the Blanks

173. All circles are __________(congruent, similar)

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174. All squares are __________ (similar, congruent)

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175. All _________ triangles are similar,(isosceles, equilateral)

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176. Two polygons of the same number of sides are similar, if (a) their corresponding angles are ________ and (b) their corresponding sides are _________(equal, proportional).

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Short Answer Type

177.

Give two different examples of pair of
(i) similar figures.
(ii) non-similar figures.

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178. State whether the following quadrilaterals are similar or not:

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179. In Fig. (i) and (ii), DE || BC. Find EC in (i) and AD in (ii).

(i) In ∆ABC, we have

space space DE parallel to BC

rightwards double arrow space space space space space space space space space space space space AD over DB equals AE over EC

[By Basic proportionality therorem]

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(ii) In ∆ABC, we have

space space space space space DE parallel to BC

rightwards double arrow

space space AD over DB equals AE over EC

[By Basic proportionality theorem]

space space rightwards double arrow space space space space space space space space space space space space space space space space space space space fraction numerator AD over denominator 7.2 end fraction equals fraction numerator 1.8 over denominator 5.4 end fraction space space rightwards double arrow space space space space space space space space space space space space space space space space space space space space space space space space space space AD space equals space fraction numerator 7.2 cross times 1.8 over denominator 5.4 end fraction equals 2.4 space cm.

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Long Answer Type

180.

E and F are points on the sides PQ and PR respectively of a ∆PQR. For each of the following cases, state whether EF || QR:
(i) PE = 3.9 cm, EQ = 3 cm, PF = 3.6 cm and FR = 2.4 cm.
(ii) PE = 4 cm, QE = 4.5 cm. PF = 8 cm and RF = 9 cm.
(iii) PQ = 1.28 cm. PR = 2.56 cm, PE = 0.18 cm and PF = 0.36 cm.

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