CIE Mathematics Paper-1: Specimen Questions 127 - 127 of 175

Question number: 127

Short Answer Question▾

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As shown in the diagram UV is parallel to YZ. XUY and XVZ are straight lines.

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

Triangle XUV and triangle XYZ are________.

(b) Angle UVZ=1050. What is the size of angle VZY?

One triangle made in another triangle

One triangle made in another triangle

Find the below given calculations by using given values of triangle

Explanation

Here,

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

Angle X is common in both so it is same, angle XUV and XYZ are corresponding angles and XVU and XZY 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:

o If all angles are same in both OR

o If all pairs of sides are in same proportion OR

o 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 UVZ=1050 , angle VZY =?

Now, VZ is straight line, so angle Z+V=1800

Z+1050=1800Z=18001050Z=750

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