Advertisements
Advertisements
Question
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
ΔLMN ≅ ΔPTR
Advertisements
Solution
By Hypotenuse Side Test
APPEARS IN
RELATED QUESTIONS
CDE is an equilateral triangle formed on a side CD of a square ABCD. Show that ΔADE ≅ΔBCE.
In ΔPQR ≅ ΔEFD then ED =
In an isosceles triangle, if the vertex angle is twice the sum of the base angles, then the measure of vertex angle of the triangle is
Which of the following is not a criterion for congruence of triangles?
If ABC and DEF are two triangles such that ΔABC \[\cong\] ΔFDE and AB = 5cm, ∠B = 40°
Observe the information shown in pair of triangle given below. State the test by which the two triangles are congruent. Write the remaining congruent parts of the triangles.
From the information shown in the figure,
In ΔABC and ΔPQR
∠ABC ≅ ∠PQR
seg BC ≅ seg QR
∠ACB ≅ ∠PRQ
∴ ΔABC ≅ ΔPQR ...`square` test
∴ ∠BAC ≅ `square` ...corresponding angles of congruent triangles.
`{:("seg AB" ≅ square),("and" square ≅ "seg PR"):}}` ...corresponding sides of congruent 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.
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 diagram, AP and BQ are equal and parallel to each other.
Prove that:
- ΔAOP ≅ ΔBOQ.
- AB and PQ bisect each other.
State, whether the pairs of triangles given in the following figures are congruent or not:
Which of the following pairs of triangles are congruent? Give reasons
ΔABC;(∠B = 70°,BC = 6cm,∠C = 50°);
ΔXYZ;(∠Z = 60°,XY = 6cm,∠X = 70°).
In the figure, RT = TS, ∠1 = 2∠2 and ∠4 = 2∠3. Prove that ΔRBT ≅ ΔSAT.
AD and BE are altitudes of an isosceles triangle ABC with AC = BC. Prove that AE = BD.
If the perpendicular bisector of the sides of a triangle PQR meet at I, then prove that the line joining from P, Q, R to I are equal.
In the figure, ∠BCD = ∠ADC and ∠ACB =∠BDA. Prove that AD = BC and ∠A = ∠B.
In ΔABC, AB = AC, BM and Cn are perpendiculars on AC and AB respectively. Prove that BM = CN.
PQRS is a quadrilateral and T and U are points on PS and RS respectively such that PQ = RQ, ∠PQT = ∠RQU and ∠TQS = ∠UQS. Prove that QT = QU.
“If two sides and an angle of one triangle are equal to two sides and an angle of another triangle, then the two triangles must be congruent.” Is the statement true? Why?
It is given that ∆ABC ≅ ∆RPQ. Is it true to say that BC = QR? Why?
