{{ drag.item.val }}
Step {{step}} of 5

The Side-Splitter Theorem

A line parallel to one side of a triangle divides the other two sides proportionally.

A B C D E {{ s1_len_AD }} {{ s1_len_DB }} {{ s1_len_AE }} {{ s1_len_EC }}
Move line UP Move line DOWN
Left Ratio:
{{ s1_len_AD }} {{ s1_len_DB }}
= {{ s1_ratio_L }}
Right Ratio:
{{ s1_len_AE }} {{ s1_len_EC }}
= {{ s1_ratio_R }}
Slide to match: Make the ratio exactly 1.00

Solve with Proportions

Drag the correct lengths to build the equation and solve for x.

A B C D E AD = {{ s2_vals.ad }} DB = {{ s2_vals.db }} AE = {{ s2_vals.ae }} EC = x
{{ item.val }}
Equation built!
{{ s2_slots.ad ? s2_slots.ad.val : 'AD' }}
{{ s2_slots.db ? s2_slots.db.val : 'DB' }}
=
{{ s2_slots.ae ? s2_slots.ae.val : 'AE' }}
x
Solve for x:

Angle Bisector Theorem

An angle bisector divides the opposite side into segments proportional to the adjacent sides.
Tap pairs of corresponding segments to match them.

A B C D Side Side Base Seg. Base Seg.
Proportion Matched!
Left Pair
Right Pair

Geometric Mean (Altitude)

The altitude to the hypotenuse divides it into segments p and q.
Theorem: The square of the altitude (h²) equals the product of segments (p × q).

Hypotenuse p = 4 q = 9 h = {{ s4_h }} p × q = 4 × 9 = 36 h² = {{ s4_h * s4_h }}
h² = 4 × 9
Areas Match!
Grow 'h' until its square area matches the rectangle.

Final Challenge

Match the missing values using the theorems.

{{ ans }}
All matched!
Side-Splitter
2 x 4 10
x =
{{ s5_answers.p1 }}
Angle Bisector
6 9 4 y
y =
{{ s5_answers.p2 }}
Altitude
4 16 z
z =
{{ s5_answers.p3 }}