Mathematics

In the following figure, $$\displaystyle \angle AXY= \angle AYX.$$ If
$$\displaystyle \frac{BX}{AX}=\frac{CY}{AY},$$ then the triangle ABC is isosceles.


ANSWER

True


SOLUTION
In $$\triangle AXY$$ and $$\triangle ABC$$,
$$\dfrac{BX}{AX} = \dfrac{CY}{AY}$$

By converse of equal intercept theorem,
$$BC \parallel XY$$

Thus, $$\angle ABC = \angle AXY$$ and $$\angle ACB = \angle AYX$$ (Corresponding angles)

Also, $$\angle AXY = \angle AYX$$ (Given)

Thus, $$\angle ABC = \angle ACB$$

hence, $$\triangle ABC$$ is an Isosceles triangle.
View Answers

You're just one step away

Create your Digital Resume For FREE on your name's sub domain "yourname.wcard.io". Register Here!


TRUE/FALSE Medium Published on 09th 09, 2020
Next Question
Questions 120418
Subjects 10
Chapters 88
Enrolled Students 86
Enroll Now For FREE

Realted Questions

Q1 Single Correct Medium
If two lines intersect such that four vertical angles are equal, then each angle is:
  • A. $$45^{\circ}$$
  • B. $$100^{\circ}$$
  • C. $$180^{\circ}$$
  • D. $$90^{\circ}$$

Asked in: Mathematics - Lines and Angles


1 Verified Answer | Published on 09th 09, 2020

View Answer
Q2 Subjective Medium
Two parallel lines $$l$$ and $$m$$ are cut by a transversal $$t$$. If the interior angles of the same side of $$t$$ are $$(2x-8)^\circ$$ and $$(3x-7)^\circ$$, find the measure of each of these angles.

Asked in: Mathematics - Lines and Angles


1 Verified Answer | Published on 09th 09, 2020

View Answer
Q3 Subjective Medium
If $$A,B$$ are complementary angles, then $$\cos ^{ 2 }{ A } +\cos ^{ 2 }{ B }$$

Asked in: Mathematics - Lines and Angles


1 Verified Answer | Published on 09th 09, 2020

View Answer
Q4 Subjective Medium
In questions $$ 1 $$ and $$ 2, $$ given below, identify the given pairs of angles as corresponding angles, interior alternate angles, exterior alternate angles, adjacent angles, vertically opposite angles or allied angles:

$$ \angle 7 \quad and \quad \angle 13 $$

Asked in: Mathematics - Lines and Angles


1 Verified Answer | Published on 09th 09, 2020

View Answer
Q5 Subjective Medium
What is an Obtuse Angle ?

Asked in: Mathematics - Lines and Angles


1 Verified Answer | Published on 09th 09, 2020

View Answer