triangles abc and apq are two equilateral triangles. pq intersects ac at m. apb is congruent to acq. the congruency is proved by

Triangles ABC and APQ are two equilateral triangles. PQ intersects AC at M. ΔAPB is congruent to ΔACQ. The congruency is proved by => SAA..

Two sides of an equilateral triangle ABC are chosen at random. What is the probability that the two sides chosen are congruent? => 1 3 or 0 or 1 or 2 3..

Isosceles triangles ABC and PQR are congruent. Angle bisectors of ∠ ABC and ∠ ACB meet at D. Angle bisectors of ∠ PQR and ∠ PRQ meet at M. With what postulate of congruency of triangles can you prove that BD ..

In ΔABC, BE ‾ and CF ‾ are the altitudes and they intersect inside the triangle at O. If AC > AB, then what is the relation between OC ‾ and OB ‾ ? => OC = 2OB or OC < OB or OC = OB or OC > OB..

Justify step 2 in the following indirect proof. Given 1). ΔABC 2). BC > AC Proof: ∠ A is not congruent to ∠ B Step 1: Assume ∠ A ≅ ∠ B Step 2: Then ΔABC is isosceles with BC ‾ = AC &Ove..

Question: ABC and ABD are two triangles such that AD=BC, BD=AC. Answer: Data: In triangles ABC and ABD, AD=BC and BD=AC. To prove: Proof: Comparing D ABC and D ABD , BC = AD (data) ..

Question: Prove that an equilateral triangle can be constructed on any given line segment. Answer: Let AB be a given line segment. According to Euclid's postulate 1, a circle can be drawn with any centre and any radius. Taking A as the centre and AB a..

Question: Show that the quadrilateral formed by joining the mid-points of the sides of a square is also a square. Answer: Given: ABCD is a square. P, Q, R and S are mid-points of AB, BC, CD and DA respectively. To prove: PQRS is also a square. Construction: Join the di..

Inequalities - If two sides of a triangle are unequal, then the greater angle is opposite to the greater side. AB > AC If two angles of a triangle are unequal, the greater side is opposite to the greater angle. AB > AC..

Thus (ii) is proved. Note: The following results can be obtained from BPT In a D ABC, DE||BC and intersects AB in D and AC in E, th..