- This is an assessment test.
- These tests focus on geometry and mensuration and are meant to indicate your preparation level for the subject.
- Kindly take the tests in this series with a pre-defined schedule.

## Geometry and Mensuration: Test 24

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Question 1 |

AB, EF and CD are parallel lines. Given that, EF= 5 cm GC = 10 cm, AB = 15 cm and DC = 18 cm. What is the value of AC?

20 cm | |

24 cm | |

25 cm | |

28 cm |

Question 1 Explanation:

Question 2 |

In the given triangle, AB is parallel to PQ. AP = c, PC = b, PQ = a, AB = x. What is the value of x?

$ \displaystyle a+\frac{ab}{c}$ | |

$ \displaystyle a+\frac{bc}{a}$ | |

$ \displaystyle b+\frac{ca}{b}$ | |

$ \displaystyle a+\frac{ac}{b}$ |

Question 2 Explanation:

$ \begin{array}{l}~ABC\text{ }is\text{ }congruent\text{ }to~PQC,\\\frac{AC}{PC}=\frac{BC}{QC}=\frac{AB}{PQ}\\=>x=\frac{AC\times PQ}{PC}=\frac{(b+c)a}{b}=a+\frac{ac}{b}\end{array}$

Question 3 |

In the given figure, QR is parallel to AB, DR is parallel to QB. What is the number of distinct pairs of similar triangles?

1 | |

2 | |

3 | |

4 |

Question 3 Explanation:

$ \displaystyle \begin{array}{l}The\text{ }triangles\vartriangle PDR\text{ }and\vartriangle PQB,\vartriangle PQR\text{ }and\vartriangle PAB,\vartriangle DRQ\text{ }and\vartriangle QBA\text{ }are\text{ }similar.\\Thus\text{ }there\text{ }are\text{ }three\text{ }possible\text{ }pairs\text{ }of\text{ }triangles.\\Correct\text{ }option\text{ }is\text{ }\left( c \right).\end{array}$

Question 4 |

If the angels of a triangle are 30°, 60° and 90°, then what is the ratio of the corresponding sides?

1: 2: 3 | |

1: 1: √2 | |

1: √3: 2 | |

1: √2: 2 |

Question 4 Explanation:

$\begin{array}{l}\tan \,60=\sqrt{3}\\Thus\text{ }the\text{ }ratio\text{ }of\text{ }corresponding\text{ }sides\text{ }=1:\text{ }\surd 3:\text{ }2\\\end{array}$

Question 5 |

I is the incentre of ∆ABC, ABC= 60

^{o}and ACB= 50^{o}. The BIC is:55 ^{o} | |

125 ^{o} | |

70 ^{o} | |

65 ^{o} |

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