CDS | Elementary Mathematics | Triangle

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Question 1

In the figure given below, PQRS is a parallelogram. PA bisects angle P and SA bisects angle S. What is angle PAS equal to?

• A60^o
• B75^o
• C90^o
• D100^o

Question 2

In a triangle ABC, the medians AD and BE intersect at G. A line DF is drawn parallel to BE such that F is on AC . If AC = 9 cm, then what is CF equal to?

• A2.25 cm
• B3 cm
• C4.5 cm
• D6 cm

Question 3

Consider the following :
ABC and DEF are triangles in a plane such that AB is parallel to DE, BC is parallel to EF and CA is parallel to FD.
Statement I : If angle ABC is a right angle, then DEF is also a right angle.
Statement II : Triangles of the type ABC and DEF are always congruent.
Which of the following is correct in respect of the above statements?

• AStatement I and Statement II are correct and statement II is the correct explanation of statement I
• BStatement I and Statement II are correct and statement II is not the correct explanation of statement I
• CStatement I is correct and statement II is incorrect
• Dstatement I is incorrect and statement II is correct

Question 4

Three straight lines are drawn through the three vertices of a triangle ABC, the line through each vertex being parallel to the opposite side. The triangle DEF is bounded by these parallel lines. Consider the following statements in respect of the triangle DEF :
1). Each side of the triangle Def is double the side of triangle ABC to which it is parallel.
2). Area of triangle DF is four times the area of triangle ABC.
Which of the above statements is/are correct?

• A1 only
• B2 only
• CBoth 1 and 2
• DNeither 1 nor 2

Question 5

in the triangle ABC, then base BC is trisected at D and E. The line through D, parallel to AB meets AC at F and line through E parallel to AC meets AB at G. Let EG and DF intersect at H. What is the ratio of the sum of the area of parallelogram AGHF and the area of the triangle DHE to the area of the triangle ABC?

• A
• B
• C
• D

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