Advertisements
Advertisements
Question
As shown in the following figure, in ΔLMN and ΔPNM, LM = PN, LN = PM. Write the test which assures the congruence of the two triangles. Write their remaining congruent parts.
Advertisements
Solution
In △LMN and △PNM
seg LM ≅ seg PN
seg LN ≅ seg PM ...(Given)
seg MN ≅ seg NM ...(Common side)
△LMN ≅ △PNM ...(SSS test)
`{:("∠LMN ≅ ∠PNM"), ("∠MLN ≅ ∠NPM"), ("∠LNM ≅ ∠PMN"):} } ...("c.a.c.t.")`
APPEARS IN
RELATED QUESTIONS
In a ΔABC, if AB = AC and ∠B = 70°, find ∠A.
If ΔABC ≅ ΔABC is isosceles with
In triangles ABC and PQR three equality relations between some parts are as follows:
AB = QP, ∠B = ∠P and BC = PR
State which of the congruence conditions applies:
In a ΔABC, if AB = AC and BC is produced to D such that ∠ACD = 100°, then ∠A =
In the given figure, AB ⊥ BE and FE ⊥ BE. If BC = DE and AB = EF, then ΔABD is congruent to
In the following example, a pair of triangles is shown. Equal parts of triangle in each pair are marked with the same sign. Observe the figure and state the test by which the triangle in each pair are congruent.
By ______ test
ΔXYZ ≅ ΔLMN
From the information shown in the figure, state the test assuring the congruence of ΔABC and ΔPQR. Write the remaining congruent parts of the triangles.
In the pair of triangles in the following figure, parts bearing identical marks are congruent. State the test and the correspondence of vertices by the triangle in pairs is congruent.
If the following pair of the triangle is congruent? state the condition of congruency:
In ΔABC and ΔPQR, BC = QR, ∠A = 90°, ∠C = ∠R = 40° and ∠Q = 50°.
In the following diagram, ABCD is a square and APB is an equilateral triangle.
(i) Prove that: ΔAPD≅ ΔBPC
(ii) Find the angles of ΔDPC.
In the following figure, OA = OC and AB = BC.
Prove that:
(i) ∠AOB = 90o
(ii) ΔAOD ≅ ΔCOD
(iii) AD = CD
The following figure has shown a triangle ABC in which AB = AC. M is a point on AB and N is a point on AC such that BM = CN.
Prove that: (i) BN = CM (ii) ΔBMC ≅ ΔCNB
Which of the following pairs of triangles are congruent? Give reasons
ΔABC;(AB = 8cm,BC = 6cm,∠B = 100°);
ΔPQR;(PQ = 8cm,RP = 5cm,∠Q = 100°).
Which of the following pairs of triangles are congruent? Give reasons
ΔABC;(∠B = 90°,BC = 6cm,AB = 8cm);
ΔPQR;(∠Q = 90°,PQ = 6cm,PR = 10cm).
In ΔABC, AB = AC and the bisectors of angles B and C intersect at point O.Prove that BO = CO and the ray AO is the bisector of angle BAC.
In the given figure ABCD is a parallelogram, AB is Produced to L and E is a midpoint of BC. Show that:
a. DDCE ≅ DLDE
b. AB = BL
c. DC = `"AL"/(2)`
Given that ∆ABC ≅ ∆DEF List all the corresponding congruent sides
Is it possible to construct a triangle with lengths of its sides as 4 cm, 3 cm and 7 cm? Give reason for your answer.
Without drawing the triangles write all six pairs of equal measures in the following pairs of congruent triangles.
∆XYZ ≅ ∆MLN
