In Delta ABC,P,Q,and R are the midpoints of o | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) By the Midpoint Theorem,the segment joining the midpoints of two sides of a triangle is parallel to the third side and half its length.Thus,$PQ =

Vedclass · Accepted Answer

Area of $\Delta PQR = \frac{1}{2} 	imes$ Area of $\Delta ABC$

Vedclass · Answer

(D) By the Midpoint Theorem,the segment joining the midpoints of two sides of a triangle is parallel to the third side and half its length.Thus,$PQ = \frac{1}{2} AC$,$QR = \frac{1}{2} AB$,and $RP = \frac{1}{2} BC$.$1$. The ratio of the sides of $\Delta PQR$ to $\Delta ABC$ is $1:2$. Thus,the perimeter of $\Delta PQR = \frac{1}{2} 	imes$ Perimeter of $\Delta ABC$. (Statement $C$ is true).$2$. The area of a triangle formed by joining the midpoints is $\frac{1}{4}$ of the area of the original triangle. Thus,Area of $\Delta PQR = \frac{1}{4} 	imes$ Area of $\Delta ABC$. (Statement $A$ is true,Statement $D$ is false).$3$. Since the sides are proportional,$\Delta PQR \sim \Delta CBA$. The correspondence $ABC \leftrightarrow QRP$ implies $\frac{AB}{QR} = \frac{BC}{RP} = \frac{AC}{PQ} = 2$,which is a similarity. (Statement $B$ is true).Therefore,the statement that is not true is $D$.

In $\Delta ABC$,$P$,$Q$,and $R$ are the midpoints of $\overline{AB}$,$\overline{BC}$,and $\overline{CA}$ respectively. Then,which of the following statements is not true?

Similar Questions

In quadrilateral $ABCD$,$\overline{AB} \parallel \overline{CD}$ and $\overline{AC} \cap \overline{BD} = \{O\}$. If $OA = 3x - 19$,$OB = x - 4$,$OC = x - 3$,and $OD = 4$,find the value of $x$.

In rhombus $PQRS$,$PR = 9$ and $QS = 12$. Find the perimeter of rhombus $PQRS$.

The correspondence $ABC \leftrightarrow XYZ$ between $\Delta ABC$ and $\Delta XYZ$ is a similarity. If $4AB = 5XY$ and $BC = 12$,find $YZ$. (in $.6$)

If $\Delta ABC \sim \Delta PQR$ under the correspondence $ABC \leftrightarrow RPQ$,and $m\angle A = 35^{\circ}$ and $m\angle B = 50^{\circ}$,find $m\angle Q$. (in $^{\circ}$)

In $\Delta ABC$,$m\angle B = 90^{\circ}$,$AB = 2x + 3$,$BC = x + 2$,and $AC = 3x - 1$. Find the value of $x$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module