is given that
AB = AC
∠C = ∠B (Angles opposite to equal sides are also equal)
In ∆ABC,
∠A + ∠B + ∠C = 180º (Angle sum property of a triangle)
90º + ∠B + ∠C = 180º
90º + ∠B + ∠B = 180º
2B = 90º
∠B = 45º
B = C = 45º
∆ABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB (see Fig. 7.34). Show that ∠ BCD is a right angle.
ABC and DBC are two isosceles triangles on the same base BC (see Fig). Show that ∠ABD = ∠ACD.
In ∆ ABC, AD is the perpendicular bisector of BC (see Fig. 7.30). Show that ∆ ABC is an isosceles triangle in which AB = AC.
ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see Fig). Show that
(i) ∆ ABE ≅ ∆ ACF
(ii) AB = AC, i.e., ABC is an isosceles triangle.
In Fig. 9.26, A, B, C and D are four points on a circle. AC and BD intersect at a point E such that ∠ BEC = 130° and ∠ ECD = 20°. Find ∠ BAC.
Look up the dictionary entries for the words sympathy, familiarity, comfort, care, and surprise. Use the information given in the dictionary and complete the table.
Noun, Adjective, Adverb, Verb, Meaning:
sympathy
familiarity
comfort
care
surprise