Advertisements
Advertisements
Question
Which of the following pairs of triangles are congruent? Give reasons
ΔABC;(BC = 5cm,AC = 6cm,∠C = 80°);
ΔXYZ;(XZ = 6cm,XY = 5cm,∠X = 70°).
Advertisements
Solution
In ΔABC and ΔXYZ
AC = XZ
BC = XY
The included angle ∠C = 80° is not equal to ∠X i.e. 70°.
Now, for ΔABC to be congruent to ΔXYZ, AB should be equal to XY and YZ should be equal to BC. Then, ∠A = ∠C and ∠X = ∠Z. So, the measure of ∠B will not be equal to ∠Y.
Therefore, ΔABC cannot be congruent to ΔXYZ.
APPEARS IN
RELATED QUESTIONS
Find the measure of each angle of an equilateral triangle.
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
ΔXYZ ≅ ΔLMN
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
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 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.
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
State, whether the pairs of triangles given in the following figures are congruent or not:
Δ ABC in which AB = 2 cm, BC = 3.5 cm and ∠C = 80° and Δ DEF in which DE = 2 cm, DF = 3.5 cm and ∠D = 80°.
In the figure, BM and DN are both perpendiculars on AC and BM = DN. Prove that AC bisects BD.
If the given two triangles are congruent, then identify all the corresponding sides and also write the congruent angles
If ∆PQR is congruent to ∆STU (see figure), then what is the length of TU?
