Question

in the figur , angle LMN=angle =90° seg MK perpendikular seg LN solve the activity to prove R is the midpoint of seg MK

Answer 1

Proof : In Triangle LMN

Angle LMN =90°

seg MR perpendicular hypt. LN

By geometric mean

MR Sq. =LR×RN...... eqn. 1

In triangle LKN, angle LKN =90°

Seg .KR perpendicular hypt. LN

By geometric. Mean

KR Sq. =LR×RN...... eqn. 2

From eqn. 1 and 2

MR Sq. =KR Sq

MR=KR

R is the midpoint of Seg.K

Answer 2

in the figure , angle LMN=angle =90° seg MK perpendicular seg LN solve the activity to prove R is the midpoint of seg MK

• Proof : In ΔLMN , ∠LMN =90° , seg MR ⊥ hypt. LN
• ∴ By geometric mean
• MR² = LR × RN...... (1)
• In ΔLKN, ∠LKN =90°, seg .KR ⊥ hypt. LN
• ∴ By property of geometric mean,
• KR² = LR × RN...... (2)
• From (1) and (2) we get
• MR² = KR²
• ∴ MR = KR
• ∴ R is the midpoint of seg MK