Question

Question was provided via image upload.

Explanation:

Step1: Fill right angle blanks

All three triangles are right triangles, so $\text{m}\angle ACB = \text{m}\angle ADC = \text{m}\angle CDB = 90^\circ$

Step2: Fill angle sum blanks

For $\triangle ACD$: $\text{m}\angle CAD + \text{m}\angle ACD = 90^\circ$; for $\triangle CBD$: $\text{m}\angle CBD + \text{m}\angle BCD = 90^\circ$

Step3: Equate complementary angles

From equal sums, $\text{m}\angle CBD = \text{m}\angle ACD$; $\text{m}\angle CAD = \text{m}\angle BCD$. Reason: Transitive property (equal to same angle sum remainder)

Step4: Prove triangle similarity

All triangles share 2 congruent angles. Reason: AA Similarity

Answer:

Statement	Reason
$\text{m}\angle CAD + \text{m}\angle CBD = 90^\circ$ <br> $\text{m}\angle CAD + \text{m}\boldsymbol{\angle ACD} = 90^\circ$ <br> $\text{m}\angle CBD + \text{m}\boldsymbol{\angle BCD} = 90^\circ$	Triangle Angle Sum Theorem
$\text{m}\angle CBD = \text{m}\boldsymbol{\angle ACD}$ <br> $\text{m}\angle CAD = \text{m}\boldsymbol{\angle BCD}$	$\boldsymbol{\text{Transitive property}}$
$\triangle ABC \sim \triangle ACD \sim \triangle CBD$	$\boldsymbol{\text{AA Similarity}}$