Question

PLEASE HELPPP

Given △ABC and altitude AH, decide whether each statement is necessarily true about △AHC. Select Yes or No for A − C.


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A. AH < HC

A Yes B No

B. AH < AC

A Yes B No

C. △AHC ≅ △AHB

Answer 1

(a) AH < HC is No

(b) AH < AC is Yes

(c) △AHC ≅ △AHB is Yes

Explanation:

Given

See attachment for triangle

Solving (a): AH < HC

Line AH divides the triangle into two equal right-angled triangles which are: ABH and ACH (both right-angled at H).

To get the lengths of AH and HC, we need to first determine the measure of angles HAC and ACH. The largest of those angles will determine the longest of AH and HC. Since the measure of the angles are unknown, then we can not say for sure that AH < HC because the possible relationship between both lines are: AH < HC, AH = HC and AH > HC

Hence: AH < HC is No

Solving (b): AH < AC

Length AC represents the hypotenuse of triangle ACH, hence it is the longest length of ACH.

This means that:

AH < AC is Yes

Solving (c): △AHC ≅ △AHB

This has been addresed in (a);

Hence:

△AHC ≅ △AHB is Yes