the altitude, $\overline{bd}$, of $\triangle abc$ is shown in the diagram.
move angles and reasons to the table to complete the proof showing that the altitude of a right triangle creates two smaller triangles that are similar to the original triangle.
$\begin{array}{|c|c|}\hline\text{statement}&\text{reason}\\\hline\angle c \cong \underline{\quad\quad}&\text{reflexive property}\\\hline m\angle abc = m\underline{\quad\quad} = 90^\circ&\text{definition of right angles}\\\hline \triangle abc \sim \triangle bdc&\underline{\quad\quad}\\\hline \angle a \cong \underline{\quad\quad}&\text{reflexive property}\\\hline m\angle abc = m\underline{\quad\quad} = 90^\circ&\text{definition of right angles}\\\hline \triangle abc \sim \triangle adb&\underline{\quad\quad}\\\hline\end{array}$
$\angle adb$ $\angle bac$ $\angle bcd$ $\angle bdc$ $\angle dba$ $\angle dbc$
aa similarity
sas similarity
sss similarity
question # 40

Question

Accepted Answer

# Explanation:
## Step1: Fill reflexive angle for ∠C
$\angle C \cong \angle BCD$
## Step2: Fill right angle for ∠ABC
$m\angle ABC = m\angle BDC = 90^\circ$
## Step3: Choose similarity rule for △ABC~△BDC
AA Similarity
## Step4: Fill reflexive angle for ∠A
$\angle A \cong \angle BAC$
## Step5: Fill right angle for ∠ABC
$m\angle ABC = m\angle ADB = 90^\circ$
## Step6: Choose similarity rule for △ABC~△ADB
AA Similarity

# Answer:
| Statement | Reason |
|-----------|--------|
| $\angle C \cong \boldsymbol{\angle BCD}$ | Reflexive property |
| $m\angle ABC = m\boldsymbol{\angle BDC} = 90^\circ$ | Definition of right angles |
| $	riangle ABC \sim 	riangle BDC$ | $\boldsymbol{AA\ Similarity}$ |
| $\angle A \cong \boldsymbol{\angle BAC}$ | Reflexive property |
| $m\angle ABC = m\boldsymbol{\angle ADB} = 90^\circ$ | Definition of right angles |
| $	riangle ABC \sim 	riangle ADB$ | $\boldsymbol{AA\ Similarity}$ |

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QUESTION IMAGE

Question

Explanation:

Step1: Fill reflexive angle for ∠C

Step2: Fill right angle for ∠ABC

Step3: Choose similarity rule for △ABC~△BDC

Step4: Fill reflexive angle for ∠A

Step5: Fill right angle for ∠ABC

Step6: Choose similarity rule for △ABC~△ADB

Answer:

Statement	Reason
$m\angle ABC = m\boldsymbol{\angle BDC} = 90^\circ$	Definition of right angles
$\triangle ABC \sim \triangle BDC$	$\boldsymbol{AA\ Similarity}$
$\angle A \cong \boldsymbol{\angle BAC}$	Reflexive property
$m\angle ABC = m\boldsymbol{\angle ADB} = 90^\circ$	Definition of right angles
$\triangle ABC \sim \triangle ADB$	$\boldsymbol{AA\ Similarity}$