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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?

Solution not provided.

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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).

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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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