Tag: triangles

Quizzes (16) Questions (4)

Questions Related to triangles

Multiple choice maths triangles relation between perimeters of similar shapes basic proportionality theorem and its converse basic proportionality theorem

In the sides $BC,CA,AB$ of a triangle $ABC$, three points $D,E,F$ are taken such that each of $BD,CE,AE$ is equal to one-third of the corresponding side, then
$\triangle DEF=\dfrac {1}{2}\triangle ABC$.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

If D, E, F divide the sides in 1:2 ratio, the area of triangle DEF is (1 - 3*(1/3)*(2/3)) = 1/3 of the area of triangle ABC. The statement that it is 1/2 is false.

Multiple choice maths triangles relation between perimeters of similar shapes basic proportionality theorem and its converse basic proportionality theorem

If $AD$ and $PM$ are medians of triangles $ABC$ and $PQR$, respectivetly where $\triangle ABC \sim \triangle PQR$, then  $\dfrac {AB}{PR}=\dfrac {AC}{PM}$.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For similar triangles, the ratio of corresponding medians is equal to the ratio of corresponding sides (AB/PQ = AD/PM). The provided ratio AB/PR = AC/PM is not a standard property of similar triangles.

Multiple choice maths triangles areas of similar figures areas of similar triangles relations between the areas of triangles

The area of two similar triangles are $200$ and $128$, then the ratio of their corresponding altitude is __________

  1. $25:16$
  2. $5:4$
  3. $4:5$
  4. $16:25$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Since we know that ratio of areas of two similar triangles is equal to the square of the ratio of their altitude
therefore
Ratio of their altitude=$\sqrt {\dfrac{{200}}{{128}}} $
$ = \sqrt {\dfrac{{100}}{{64}}} $
$ = \dfrac{{10}}{8}$
$ = \dfrac{5}{4}$
$ = 5:4$