Question

1. choose the correct answer.

which triangle involves altitudes?

Explanation:

Step1: Recall the definition of altitude

An altitude of a triangle is a perpendicular segment from a vertex to the line containing the opposite side.

Step2: Analyze each option

• Option A: Shows medians (segments from vertex to mid - point of opposite side) as \(AX = XC\), \(BY\) and \(CZ\) are also likely medians (since \(AP=\frac{1}{3}AZ\) etc. is a property of centroid related to medians).
• Option B: Shows angle - bisectors (marked with angle - bisector symbols).
• Option C: \(BY\perp AC\), \(BZ\perp AC\) (right - angle symbols at \(Y\) and \(Z\) with respect to sides of the triangle), \(AX\perp BC\). These are altitudes as they are perpendicular from vertices to the opposite sides.
• Option D: Shows perpendicular bisectors (since \(AP = BP=CP\) is a property related to circum - center which is the intersection of perpendicular bisectors).

Answer:

C.