Advertisements
Advertisements
Question
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.
Solution
The triangles are congruent by the SAA or ASA test, under the correspondence MTN ↔ STN.
RELATED QUESTIONS
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.
Prove that the sum of three altitudes of a triangle is less than the sum of its sides.
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 triangles ABC and PQR, if ∠A = ∠R, ∠B = ∠P and AB = RP, then which one of the following congruence conditions applies:
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 given figure, seg AB ≅ seg CB and seg AD ≅ seg CD. Prove that ΔABD ≅ ΔCBD.
In the following diagram, AP and BQ are equal and parallel to each other.
Prove that:
(i) ΔAOP≅ ΔBOQ.
(ii) AB and PQ bisect each other.
The following figure 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: ΔAMC≅ ΔANB
Which of the following pairs of triangles are congruent? Give reasons
ΔABC;(AB = 5cm,BC = 7cm,CA = 9cm);
ΔKLM;(KL = 7cm,LM = 5cm,KM = 9cm).
“If two angles and a side of one triangle are equal to two angles and a side of another triangle, then the two triangles must be congruent.” Is the statement true? Why?
