Login
Home
TOP
Send feedback
Login
Subjects
Maths CBSE Live product
Class 9
Quadrilateral
Properties of Quadrilaterals I
4.
Prove the given statement
Question:
3
m.
In a quadrilateral \(KLMN\), \(KN = LM\) and \(\angle KNM = \angle LMN\). If \(P\) is the mid-point of \(MN\), then prove that \(KP = LP\).
S. No
.
Statement
Reason
1
.
\(KM = LN\)
\(KN = LM\)
\(KL = MN\)
Given
2
.
\(\angle KPN = \angle LPM\)
\(\angle KNP = \angle LMP\)
\(\angle KPM = \angle LPN\)
Since \(\angle KNM = \angle LMN\)
Since \(\angle KMN = \angle LNM\)
3
.
\(KP = LP\)
\(NP = MP\)
\(\angle KNM = \angle LMN\)
\(P\) is the mid-point of \(MN\)
4
.
\(\Delta KNP \cong \Delta LMP\)
\(\Delta KNM \cong \Delta LMN\)
by \(SAS\) congruence rule
by \(SSS\) congruence rule
by \(ASA\) congruence rule
5
.
\(KP = LP\)
\(KL = LM\)
\(KL = MN\)
by CPCT
Hence, proved
.
Login
or
Fast registration
Previous task
Exit to the topic
Next task
Send feedback
Did you find an error?
Send it to us!
