Advertisements
Advertisements
Question
If figure OPRQ is a square and ∠MLN = 90°. Prove that ∆LOP ~ ∆RPN
Solution
In ∆LOP and ∆RPN
∠OLP = ∠PRN = 90°
∠LPO = ∠PNR ...(OP || MN)
∴ ∆LOP ~ ∆RPN ...(By AA similarity)
APPEARS IN
RELATED QUESTIONS
In figure, ∆ACB ~ ∆APQ. If BC = 8 cm, PQ = 4 cm, BA = 6.5 cm, AP = 2.8 cm, find CA and AQ.
State the SSS-similarity criterion for similarity of triangles
In the following figure, point D divides AB in the ratio 3 : 5. Find :
BC = 4.8 cm, find the length of DE.
Prove that, if a line is drawn parallel to one side of a triangle to intersect the other two sides, then the two sides are divided in the same ratio.
D and E are points on the sides AB and AC respectively of a Δ ABC such that DE | | BC and divides Δ ABC into two parts, equal in area. Find `"BD"/"AB"`.
In the figure, AB || RQ and BC || SQ, prove that `"PC"/"PS" = "PA"/"PR"`.
PQ is perpendicular to BA and BD is perpendicular to AP.PQ and BD intersect at R. Prove that ΔABD ∼ ΔAPQ and `"AB"/"AP" = "BD"/"PQ"`.
In a quadrilateral PQRS, the diagonals PR and QS intersect each other at the point T. If PT:TR = QT :TS = 1:2, show that TP:TQ = TR:TS
In fig. BP ⊥ AC, CQ ⊥ AB, A−P−C, and A−Q−B then show that ΔAPB and ΔAQC are similar.
In ΔAPB and ΔAQC
∠APB = [ ]° ......(i)
∠AQC = [ ]° ......(ii)
∠APB ≅ ∠AQC .....[From (i) and (ii)]
∠PAB ≅ ∠QAC .....[______]
ΔAPB ~ ΔAQC .....[______]
Observe the figure and complete the following activity
In fig, ∠B = 75°, ∠D = 75°
∠B ≅ [ ______ ] ...[each of 75°]
∠C ≅ ∠C ...[ ______ ]
ΔABC ~ Δ [ ______ ] ...[ ______ similarity test]