Extension (as a definition) increases the angle between the bones in a joint.  When you extend your knee, you are straightening your knee from the bent position, increasing the angle between the femur and the shin bones.  When you are extending your hip, your leg is essentially moving backwards in space, say 10-20 degrees.  When you walk, run, or lunge, you have one hip passing through extension.  Now why the fuss about these two words?
To start, get into a lunge position with your right knee up and your left knee on the floor. Rest your hands on the ground, directly underneath your shoulders. Next, flex your raised right knee outward, so that you’re resting on the outside of your right foot. Press your chest forward to increase the stretch. Hold this pose for 10 seconds, then repeat on the other side of your body.
Gait analysis studies in the elderly show that they typically have a shortened step length. Whether that is a result of tight hip flexors or due to reduced balance, the propensity to walk with shorter steps will itself lead to tightness in hip flexors and anterior joint structures. Hip stretches may be a relatively easy preventative strategy for the elderly with gait abnormalities and may help to prevent falls.
It's easy to compensate in this position by hyperextending your lower back, but it's crucial that you don't. Instead, I want you to focus on squeezing your glutes and hamstrings, which will push your hips forward into a full-on "schwing." If your right foot is back, you should feel an intense stretch on the right front side of your hip. Hold it for a long time, like a minute or two, and then switch sides.
If most inner-thigh openers feel too easy (and your ankles and knees are injury-free), try Frog Pose. Get down on all fours, with palms on the floor and your knees on blankets or a mat (roll your mat lengthwise, like a tortilla, and place it under your knees for more comfort). Slowly widen your knees until you feel a comfortable stretch in your inner thighs, keeping the inside of each calf and foot in contact with the floor. Make sure to keep your ankles in line with your knees. Lower down to your forearms. Stay here for at least 30 seconds.
How to: Lie on your back with your right knee bent and foot flat on the floor (a). Extend your left leg up to the ceiling and wrap a strap around the sole of your left foot (b). While holding both ends with your left hand, extend your right arm directly out to the side in order to anchor yourself (c). Slowly let the left leg fall toward the left while keeping your right side grounded. Hold for six to eight breaths, then repeat on the opposite side.
The rectus femoris is one of the quadriceps muscles. The rectus femoris arises from the front of your hipbone, runs through the middle region of the front thigh and attaches to the top of the kneecap. In addition to hip flexion, the rectus femoris straightens, or extends, your knee. This dual function increases the vulnerability to strain injuries. Stretching exercises to maintain flexibility and balanced training to equalize your quad and hamstring strength reduce the likelihood of rectus femoris strains.

To achieve this stretch, start out on your hands and knees. Slowly widen your knees out as far as they can go, and make sure to keep your lower legs in line with your knees. Your lower legs and feet should be parallel with one another. Next, ease your upper body forward on your forearms and reach forward until you feel the stretch. Hold this pose for about 10 seconds.
How to: Lie on your back with your right knee bent and foot flat on the floor (a). With your left leg fully extended, press into your right foot to shift onto your left hip. This is your starting position (b). Then, squeeze your right glutes to press your left hip open until you feel a stretch, pause, then return to start. That’s one rep (c). Perform six to eight reps, then repeat on the opposite side.
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