Advertisements
Advertisements
Question
In the following figure, M is the mid-point of both AC and BD. Then ______.
Options
∠1 = ∠2
∠1 = ∠4
∠2 = ∠4
∠1 = ∠3
Advertisements
Solution
In the following figure, M is the mid-point of both AC and BD. Then ∠1 = ∠4.
Explanation:
In ΔAMB and ΔCMD,
AM = CM ...[M is the mid-point]
BM = DM ...[M is the mid-point]
∠AMB = ∠CMD ...[Vertically opposite angles]
By SAS congruence criterion,
ΔAMB ≅ ΔCMD
∴ ∠1 = ∠4 ...[By C.P.C.T]
APPEARS IN
RELATED QUESTIONS
To conclude the congruency of triangles, mark the required information in the following figure with reference to the given congruency criterion
Construct a triangle ABC with given conditions.
AB = 7 cm, AC = 6.5 cm and ∠A = 120°
Construct a triangle PQR with given conditions.
∠P = 60°, ∠R = 35° and PR = 7.8 cm
Construct a triangle PQR with given conditions.
∠Q = 90°, ∠R = 42° and QR = 5.5 cm
In ∆ABC and ∆PQR, ∠A = 50° = ∠P, PQ = AB, and PR = AC. By which property ∆ABC and ∆PQR are congruent?
Using the given figure, prove that the triangles are congruent. Can you conclude that AC is parallel to DE
In the following figure, two triangles are congruent by RHS.
In the following figure, which pairs of triangles are congruent by SAS congruence criterion (condition)? if congruent, write the congruence of the two triangles in symbolic form.
In the following figure, which pairs of triangles are congruent by SAS congruence criterion (condition)? if congruent, write the congruence of the two triangles in symbolic form.
State which of the following pairs of triangles are congruent. If yes, write them in symbolic form (you may draw a rough figure).
∆PQR: PQ = 3.5 cm, QR = 4.0 cm, ∠Q = 60°
∆STU: ST = 3.5 cm, TU = 4 cm, ∠T = 60°
