If D is the midpoint of BC in △ABC and ∠A = 90⁰, then AD = _______.

In △ABC, AB = AC = 12 cm, BC = 5 cm and D is a point on AC such that DB = BC. What is the measure of CD?

A right-angled triangle has a hypotenuse of 13 cm and one leg of 5 cm. A second right-angled triangle is similar to the first, and its hypotenuse is 39 cm. What is the area of the second triangle?

In a quadrilateral ABCD, a line segment BD is a diagonal such that AB=CD and ∠ABD=∠CDB. Are the triangles ABD and CDB congruent? If so, by what rule?

In a trapezoid ABCD with AB parallel to CD, the diagonals AC and BD intersect at E. What is the ratio of the area of △ABE to the area of △CDE?

Two right-angled triangular blocks, ABC and DEF, have ∠B = ∠E = 90°. If the lengths of the hypotenuses AC and DF are equal, and the sides AB and DE are equal, are the triangles congruent? If so, by what rule?

A right triangle ABC is inscribed in a circle with a diameter of 10 cm. An altitude BD is drawn from the vertex B to the hypotenuse AC. If the length of the leg AB is 6 cm, what is the length of the segment AD?

In a triangle ABC, medians AD and BE intersect at G. If the length of median AD is 12 cm, what is the length of the segment AG?

In ∆ABC, a line segment DE is parallel to BC, with D on AB and E on AC. If the ratio of the area of △ADE to the area of the trapezoid DECB is 4 : 21, what is the ratio of AD to DB?

In triangle ABC, medians AD, BE, and CF intersect at the centroid G. What is the ratio of the area of triangle GAB to the area of triangle ABC?

In △ABC, BD ⟂ AC at D and ∠DBC = 25°. E is a point on BC such that ∠CAE = 80°. What is the measure of ∠AEB?