Advertisements
Advertisements
प्रश्न
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 triangles in each pair are congruent.
By ______ test
ΔPRQ ≅ ΔSTU
Advertisements
उत्तर
By ASA Test
APPEARS IN
संबंधित प्रश्न
In two right triangles one side an acute angle of one are equal to the corresponding side and angle of the othe Prove that the triangles are congruent.
In a ΔABC, if AB = AC and BC is produced to D such that ∠ACD = 100°, then ∠A =
In the given figure, ABC is a triangle in which ∠B = 2∠C. D is a point on side BC such that ADbisects ∠BAC and AB = CD. BE is the bisector of ∠B. The measure of ∠BAC is
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
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
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.
Prove that:
(i) ∆ ABC ≅ ∆ ADC
(ii) ∠B = ∠D
(iii) AC bisects angle DCB
Prove that:
(i) ∆ ABC ≅ ∆ ADC
(ii) ∠B = ∠D
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 a circle with center O. If OM is perpendicular to PQ, prove that PM = QM.
In ΔABC and ΔPQR and, AB = PQ, BC = QR and CB and RQ are extended to X and Y respectively and ∠ABX = ∠PQY. = Prove that ΔABC ≅ ΔPQR.
In a triangle ABC, if D is midpoint of BC; AD is produced upto E such as DE = AD, then prove that:
a. DABD andDECD are congruent.
b. AB = EC
c. AB is parallel to EC
In the figure, BM and DN are both perpendiculars on AC and BM = DN. Prove that AC bisects BD.
In ΔPQR, LM = MN, QM = MR and ML and MN are perpendiculars on PQ and PR respectively. Prove that PQ = PR.
AD and BE are altitudes of an isosceles triangle ABC with AC = BC. Prove that AE = BD.
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.
In the given figure, AB = DB and AC = DC. Find the values of x and y.
Given that ∆ABC ≅ ∆DEF List all the corresponding congruent sides
Given that ∆ABC ≅ ∆DEF List all the corresponding congruent angles
