CIE Mathematics Paper-1: Specimen Questions 81 - 81 of 175

Question number: 81

Short Answer Question▾

Write in Short

As shown in the diagram DE is parallel to BC. ADB and AEC are straight lines.

(a) Fill in the blanks with any of the words given: Congruent equilateral isosceles similar

Triangle ADE and triangle ABC are________.

(b) Angle BDE=1350. What is the size of angle DBC?

Two triangles made by a middle line

Two triangles made by a middle line

Find the below given calculations by using given values of triangle

Explanation

Here,

(a) Here, Triangle ADE is similar to triangle ABC because there all three angles are same in both as below:

Angle A is common in both so it is same, angle ADB and ABC are corresponding angles and AED and ACB are also corresponding angles, so these will be also same.

While both have no equal sides, so it can’t be called as congruent triangles.

  • Two triangles are called as similar triangles:
  • If all angles are same in both OR
  • If all pairs of sides are in same proportion OR
  • If two pairs of sides are in same proportion and one angle is also same in both.
  • Two triangles are called as congruent triangles when both have all equal sides and equal angles.
  • A triangle with two equal sides and the angles opposite the equal sides are also equal is called as Isosceles.

(b) Here, angle BDE=1350 , angle DBC =?

Now, BD is straight line, so angle B+D=1800

B+1350=1800B=18001350B=450

So, angle DBC = 450

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