How do you do this proof? "In circle O, line segment ABC and line segment ADE are secants. Prove that angle ADC is congruent to angle ABE.
This is the diagram:
img523.imageshack.us/my.php?image=diagram3.jpg
As I view your figure at that site, it looks like ABC and ADE are NOT line segments. Points B and D are on the circle but not on a line. The two "angles" ADC and ABE do not look like angles in the figure
AS1
how to identfy angles
Use your new 30– 60– 90 and 45– 45– 90 triangle patterns to quickly find the lengths of the missing sides in each of the triangles shown.
To prove that angle ADC is congruent to angle ABE, we need to use the properties of secants intersecting a circle.
Here are the steps to prove the statement:
Step 1: Given that line segment ABC and line segment ADE are secants intersecting circle O.
Step 2: By the intersecting secant theorem, we know that the measure of angle ADC is equal to one-half the difference of the intercepted arcs AD and BC.
Step 3: Similarly, by the intersecting secant theorem, we know that the measure of angle ABE is equal to one-half the difference of the intercepted arcs AB and DE.
Step 4: From the diagram given, we can observe that arcs AD and DE, and arcs BC and BA are congruent (as they are intercepted by the same secants).
Step 5: Using the same logic, we can also conclude that arcs AB and BC, and arcs DE and AD are congruent.
Step 6: Since arcs AD and BC, and arcs AB and DE are congruent, their differences (intercepted by angles ADC and ABE) are also congruent.
Step 7: Therefore, the measure of angle ADC is congruent to the measure of angle ABE.
By following these steps, we have proven that angle ADC is congruent to angle ABE.