Advertisements
Advertisements
प्रश्न
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 ΔPTQ and ΔSTR
seg PT ≅ seg ST
∠PTQ ≅ ∠STR ...[Vertically opposite angles]
∴ ΔPTQ ≅ ΔSTR ...`square` test
∴ `{:("∠TPQ" ≅ square),("and" square ≅ "∠TRS"):}}` ...corresponding angles of congruent triangles
seg PQ ≅ `square` ...corresponding sides of congruent triangles
Advertisements
उत्तर
From the information shown in the figure, in ΔPTQ and ΔSTR
seg PT ≅ seg ST
∠PTQ ≅ ∠STR ...Vertically opposite angles
∠PTQ ≅ ∠STR ...SAS test
∴ `{:("∠TPQ" ≅ bbunderline("∠TSR")),(bbunderline("∠TQP")≅ "∠TRS"):}}` ...[corresponding angles of congruent triangles]
seg PQ ≅ seg SR ...[corresponding sides of congruent triangles]
APPEARS IN
संबंधित प्रश्न
In a squared sheet, draw two triangles of equal areas such that
The triangles are congruent.
What can you say about their perimeters?
Prove that the sum of three altitudes of a triangle is less than the sum of its sides.
In the given figure, if AB = AC and ∠B = ∠C. Prove that BQ = CP.
If ABC and DEF are two triangles such that ΔABC \[\cong\] ΔFDE and AB = 5cm, ∠B = 40°
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 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 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 pair of triangles given below, the parts shown by identical marks are congruent. State the test and the one-to-one correspondence of vertices by which the triangles in the pair are congruent, the remaining congruent parts.
In the pair of triangles given below, the parts shown by identical marks are congruent. State the test and the one-to-one correspondence of vertices by which the triangles in the pair are congruent, the remaining congruent parts.
State, whether the pairs of triangles given in the following figures are congruent or not:
In the given figure P is a midpoint of chord AB of the circle O. prove that OP ^ AB.
In a circle with center O. If OM is perpendicular to PQ, prove that PM = QM.
AD and BE are altitudes of an isosceles triangle ABC with AC = BC. Prove that AE = BD.
In ΔABC, X and Y are two points on AB and AC such that AX = AY. If AB = AC, prove that CX = BY.
In the figure, AC = AE, AB = AD and ∠BAD = ∠EAC. Prove that BC = DE.
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 ΔABC, AB = AC. D is a point in the interior of the triangle such that ∠DBC = ∠DCB. Prove that AD bisects ∠BAC of ΔABC.
O is any point in the ΔABC such that the perpendicular drawn from O on AB and AC are equal. Prove that OA is the bisector of ∠BAC.
The top and bottom faces of a kaleidoscope are congruent.
Without drawing the triangles write all six pairs of equal measures in the following pairs of congruent triangles.
∆ABC ≅ ∆LMN
