Prove f statistic in ANOVA multiple regression equals t statistic in linear regression

To clarify what I mean, let's say we have these two models

fit.1<-lm(Output~Input1)
fit.1.2<-lm(Output~Input1+Input2)

Running anova(fit.1,fit.1.2) will provide an f-statistic for Input2 and the p-value for it's significance. Running summary(fit.1.2) will provide a t-statistic for Input1 and Input2 and the p-value for both. My question is why is the p-value for the f-statistic of Input2 in the ANOVA test equal to the p-value of the t-statistic of Input2 in the t-test? Below, I have attempted to include the output.

> anova(fit.1,fit.1.2)
Analysis of Variance Table
Model 1: Output ~ Input1
Model 2: Output ~ Input1 + Input2
Res.Df   RSS Df  Sum of Sq  F Pr(>F)
1    498 185.43
2    497 185.38  1    0.0452 0.1212 0.7279

> summary(fit.1.2.3)
Call:
lm(formula = Output ~ Input1+Input2)
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)  1.21480    0.05179  23.458   <2e-16
Input1       0.80116    0.02819  28.423   <2e-16
Input2       0.00970    0.02787   0.348    0.728