Ratio of the heights of two similar cones is 7/9
what is the ratio of their radii? ratio of their volumes??
If they are similar, the ratio of the radaii is the same.
Now consider that the volume of a cone is 1/3 PI r^2 * h
So the volume ratio will have a (7/9)^2 * 7/9 ratio
Criteria for Congruence of triangles.
We are given the triangles ABC and ADC. As clear from the name, the both the triangles have a common side AC.
Criterion that can be used for congruence:
When all the three sides of the triangle is equal to corresponding three sides of other triangle.
When two sides and one angle of triangle is equal to the corresponding sides and angle of other triangle.
When two angles and one side of triangle is equal to the corresponding angles and side of other triangle.
In triangles ABC and ADC,Angles BCA and DAC are congruent (from the diagram);Angles BAC and DCA are congruent (from the diagram);AC is congruent AC (by reflexive property).
So, the triangles ABC and CDA are congruent by ASA postulate.
ASA (Angle-Side-Angle) postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.
So, triangles ABC and ADC are congruent by ASA.