Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of ∆ PQR (see Fig. 7.40). Show that:
(i) ∆ BM≅∆ PQN
(ii) ∆ ABC≅∆ PQR
(i) In ∆ABC, AM is the median to BC.
∠ BM=\(\frac{1}{2} \) BC
∠QN= \(\frac{1}{2} \) QR
However, BC =QR
∠BC=\(\frac{1}{2} \) QR= \(\frac{1}{2} \)
∠BM=QN ….(1)
In ∆ABM and ∆PQN,
In ∆PQR, PN is the median to QR.
AB = PQ (Given)
BM = QN [From equation (1)]
AM = PN (Given)
∠∆ABM ≅ ∠∆PQN (SSS congruence rule)
∠ABM = ∠PQN (By CPCT)
∠ABC =∠PQR … (2)
(ii) In ∆ABC and ∆PQR,
AB = PQ (Given)
∠ABC = ∠PQR [From equation (2)]
BC = QR (Given)
∠∆ABC ≅ ∠∆PQR (By SAS congruence rule)
Use these adverbs to fill in the blanks in the sentences below.
awfully sorrowfully completely loftily carefully differently quickly nonchalantly
(i) The report must be read ________ so that performance can be improved.
(ii) At the interview, Sameer answered our questions _________, shrugging his shoulders.
(iii) We all behave _________ when we are tired or hungry.
(iv) The teacher shook her head ________ when Ravi lied to her.
(v) I ________ forgot about it.
(vi) When I complimented Revathi on her success, she just smiled ________ and turned away.
(vii) The President of the Company is ________ busy and will not be able to meet you.
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