State true or false-In displaystyle Delta ABC- D and E are the points on sides AB and AC respectively- If AB- 9 cm- AD- 4 cm- AE-6 cm and EC- 7-5 cm- then DE parallel BC-TrueFalse

Question

Toppr Admin · Accepted Answer

In -x25B3-ABC-xA0-AD-4cm-AB-9cm-EC-7-5cm-AE-6cm-xA0-AD-DB-9-ABDB-9-x2212-4-5ADDB-45-AEEC-67-5-45-x2234- By basic proportionality theorem-xA0-DE-x2225-BC

State true or false:
In $Δ A B C$ , D and E are the points on sides AB and AC respectively. If $A B = 9 c m, A D = 4 c m, A E = 6 c m$ and $E C = 7.5 c m$ , then $D E ∥ B C$ .

True
False

In $△ A B C$ ,
$A D = 4 c m, A B = 9 c m, E C = 7.5 c m, A E = 6 c m$
$A D + D B = 9 = A B$
$D B = 9 - 4 = 5$
$\frac{A D}{D B} = \frac{4}{5}, \frac{A E}{E C} = \frac{6}{7.5} = \frac{4}{5}$
$∴$ By basic proportionality theorem,
$D E ∥ B C$

State true or false:In ΔABC, D and E are the points on sides AB and AC respectively. If AB=9cm,AD=4cm,AE=6cm and EC=7.5cm, then DE∥BC.TrueFalse

In △ABC, AD=4cm,AB=9cm,EC=7.5cm,AE=6cm AD+DB=9=ABDB=9−4=5ADDB=45,AEEC=67.5=45∴ By basic proportionality theorem, DE∥BC

State true or false:
In $Δ A B C$ , D and E are the points on sides AB and AC respectively. If $A B = 9 c m, A D = 4 c m, A E = 6 c m$ and $E C = 7.5 c m$ , then $D E ∥ B C$ .

True
False

In $△ A B C$ ,
$A D = 4 c m, A B = 9 c m, E C = 7.5 c m, A E = 6 c m$
$A D + D B = 9 = A B$
$D B = 9 - 4 = 5$
$\frac{A D}{D B} = \frac{4}{5}, \frac{A E}{E C} = \frac{6}{7.5} = \frac{4}{5}$
$∴$ By basic proportionality theorem,
$D E ∥ B C$